Beatrice Lamwaka was not yet a teenager when her 13-year-old brother, Richard, was abducted as a child soldier. The family lived in Alokolum, a town in northern Uganda, an area riven by civil war and brutal uprisings since the late 1980s, and Richard was snatched by the Lord's Resistance Army (LRA), a militia group under the fanatical control of the murderous Joseph Kony. Under Kony's rule, child soldiers such as Richard were given automatic weapons and trained to kill. They were forced to commit atrocities against their friends and siblings. Those who attempted to escape were murdered.

Against all odds, Richard survived, returning home some months later. Yet he never once spoke about what he had endured. Nor did his family ever ask him what had happened. They didn't know how to tell him that in his absence, they had assumed he was dead and had buried his "tipu" – his soul.

Then, at the age of 15, Richard died of pneumonia. His mother couldn't find the words to grieve; she retreated into silence. Beatrice, too, knew not to say anything. Her childhood had been marked by violence. She grew so used to the sound of gunshot fire being exchanged between LRA rebels and government troops that she could distinguish when a bullet had hit a person and when it hadn't from the noise it made. The people in her village did not talk about such things. No one did. Silence was the only form of survival.

"They would talk about almost anything else," Lamwaka says now, more than 20 years later, sitting on her bed in her modest, single-storey home an hour's drive from Kampala. "But they wouldn't talk about what was going on around them."

It was only as an adult that Lamwaka found a way to express what she had been through and it came in the form of short stories. "The only way I could deal with it was to write the stories we hadn't been able to tell," she explains.

Lamwaka, 35, is one of a new wave of Ugandan fiction writers. Her work has been published in several anthologies and she has been nominated for several international prizes. The tale of her brother's abduction inspired a powerful short story called "Butterfly Dreams", in which a young girl is abducted by the LRA: "You caressed your scars as if to tell us what you went through," Lamwaka writes. "We did not ask questions."

Lamwaka says she has only had the confidence to turn her experiences into fiction because of the pioneering work of Femrite, an NGO established in Uganda in 1995 to promote and publish women's writing. Until that point, the literary scene in the country had been limited – publishing houses preferred to print profitable textbooks than novels that didn't sell – and what there was of it was dominated by men.

Femrite has changed all that. The organisation holds regular writing workshops and residential retreats, as well as running its own publishing arm, and is one of numerous organisations in developing countries working with Commonwealth Writers, a development foundation in the UK, which aims to unearth and nurture less-heard voices from across the Commonwealth; it also awards an annual prize for a best unpublished short story worth £5,000. The winner of the 2013 Commonwealth Short Story prize will be announced this week by John le Carré at the Hay festival.

The aim, according to Lucy Hannah, the programme manager of the Commonwealth Foundation, is "to give a platform to emerging talent, often writing from difficult places and about difficult issues. We work with local communities to ensure these writers get the recognition they deserve and can make crucial connections with other authors and publishers at an international level. In doing so, we hope to encourage a new generation of storytellers whose fiction will open up a new world to readers who might not otherwise come across their work."

Back in Uganda, a light morning breeze causes the net curtains to billow into Lamwaka's living room. Along one wall, there is a bookshelf crammed tightly with dogeared copies of novels by Chinua Achebe, Zadie Smith and Chimamanda Ngozi Adichie. One day, Lamwaka hopes her work will be there too. "It's so important for Ugandan writers to get international recognition," she explains. "We need role models."

The act of putting words on a page, of telling the truth through fiction, is a brave one for women in Uganda. It takes a particular courage to do so in a society riven by the kind of silent trauma described by Lamwaka and where the struggle for gender equality continues. In rural areas, the education of boys is still prioritised and many girls drop out of school to help in the home or to get married. As a result, they have a lower literacy rate than men. Domestic violence is high. According to figures from the Uganda Bureau of Statistics in 2007, 68% of married women aged 15 to 49 had experienced some form of violence by their spouse or intimate partner. Most women do not report such abuse to the authorities through fear of social rejection and the police rarely intervene or investigate.

Female genital mutilation (FGM) is in decline, but still a problem in the country's villages. According to Unicef, 1% of all Ugandan women aged 15-49 have been cut, leading to serious physical and psychological health issues. In 2009, Femrite volunteers travelled around the country to collect first-hand testimonies from women who had undergone female circumcision and who were, in many cases, illiterate and unable to write their own stories.

The resulting anthology, Beyond the Dance, makes powerful reading. One woman, Judith, recalls being circumcised without anaesthetic in 1976, then forced to walk 4km to a local nursing home, where she slept on a bare floor for a week before she was allowed to bathe herself.

"Unless a woman was circumcised, she would not get married," Judith says. "She would be subjected to all sorts of ridicule and, finally, she would be circumcised by force. Circumcision was not something a woman chose to do; it was what she had to do."

Judith is now paralysed from the waist down and uses a wheelchair, a situation she believes was triggered by the botched circumcision. Her husband left her because "he had no use for a crippled wife". Without Femrite, her story would never have been told.

In a bustling cafe in the Kisementi district of Kampala, Beverley Nambozo Nsengiyunva, a Femrite volunteer and poet, describes it as "the voice of silence": the inbuilt fear and shame that holds women back from telling their stories.

"In the villages, they feel it's a form of betrayal to express themselves because they're so used to silence, to just nodding without argument," she says. "They will think it's a betrayal of trust to their elders and society. But also they're scared. They think, 'If I tell the story of how this society turned against me and ruined my life through FGM, they will cast me out.' Femrite is really about creating a safe space for speaking out."

Traditionally, Ugandan women are the storytellers and keepers of the oral tradition but it takes a considerable leap of consciousness to become a writer.

"Some of these women have the basic talent to tell stories," says Goretti Kyomuhendo, a founding member of Femrite. "What is lacking is personal empowerment: self-belief, self-confidence and I think I would say they're suffering a kind of identity crisis. In many African societies, the woman's identity is constructed using that of another person: for example, if you're a woman with a baby, you become known as mama – it's a mark of cultural respect."

At one of Femrite's early workshops, Kyomuhendo recalls a woman writing "a beautiful story in the first person. It started, 'I was raped on my wedding night.'" When the woman returned the next week, she had rewritten the story in the third person, in the voice of a character called Angella. "It had no impact," says Kyomuhendo. "I asked her why she'd done it and she said, 'Because my husband said people would think it was me.' So the challenge is: how do you empower that woman to tell that story?"

Doreen Baingana, whose book Tropical Fish won the Commonwealth Writers prize for best first book in 2006, describes Femrite as "my literary home". "There are certain things in this society that are not meant to be said," she explains when we meet near her home in Entebbe on the Lake Victoria peninsula. "There are roles that women are not meant to play because of unspoken rules. Femrite provides a focus for those challenges because when we're together as women, we communicate differently."

But it would be wrong to assume that these writers are trapped in the past. While many Ugandan authors are doubtless influenced by their country's troubled history – the turbulent political upheavals and decades of civil war, the dictatorial rule of Idi Amin and his ruthless oppression of dissent – there are also those, including Baingana, who are keen to move on.

"I think we expect the African story to be one of tragedy and despair and how people overcame suffering," she says, sipping on her latte. "In fact, there are other stories. My experience growing up here wasn't horrific, even though Idi Amin was in power. For me, I just went to school and Entebbe was beautiful and green and peaceful like this." She sweeps her hand, taking in the acacia trees and the lush, verdant landscape.

The themes in Baingana's fiction are more universal – Tropical Fish is a series of interlinked short stories exploring the coming of age of three sisters – and are influenced by more recent developments in modern Uganda. In one chapter, sexually precocious oldest sister Rosa writes a letter to a former boyfriend who gave her HIV.

"Do you remember when exactly it got a name, became real?" Rosa asks. "How did we first hear about it? Rumours, whispers of strange symptoms in villages far away from us… Stories of its power spread and grew like tree roots, curling out of the ground; abnormal, ugly, strong."

Baingana says that the character of Rosa was directly influenced by her experience of university in Uganda in the late 1980s: "So many people were dying and we didn't know why. There was a period when it was a complete mystery. People said it was witchcraft. It started off with village people but then it moved and ran through all society. I wanted this story to be a record of those who died, especially those who thought it was a crime, who carried a social stigma because of a lack of understanding. In families, it was a silent disease. If a child fell sick because of it, no one would say."

Yet, despite an increased openness and awareness in the urban centres of Uganda, there are still some stories that cannot be told. Homosexuality, for instance, is illegal here. An anti-homosexuality bill currently being debated in parliament initially proposed the death penalty for those found guilty of "aggravated homosexuality", defined as when one of the participants is a minor, HIV-positive, disabled or a "serial offender". That was dropped in favour of harsher punishments for gay acts. Known colloquially as the "kill the gays" bill, it would also make it a crime not to report someone you know to be a practising homosexual, thereby putting parents, siblings and friends at risk. President Obama has described the bill as "odious".

Gay men and women face harassment, extortion, vandalism, death threats and violence on a daily basis. They can be sacked from employment if they are outed, forced to enter into heterosexual marriage and detained by the authorities without charge or access to a lawyer. In some of the worst cases, they can be subjected to "correctional rape".

Jo Jothams (not her real name) is a Femrite volunteer and a lesbian. She has known she was gay since she was 13 and developed a crush on a girl at boarding school. And yet, for more than 20 years, she has lied to friends and family about her sexuality for her own protection.

"I fear to tell my mother," Jothams says. "I think I love her too much to tell her because she might break down and be like the rest of them. People here think homosexuality is for people who are bad or evil."

The reality of being gay in Uganda is a terrifying one. Jothams talks in a low voice about a lesbian friend who was raped by a man she didn't want to marry, about her girlfriend, who was forced out of her rented apartment by the landlord and about the people she knows who have lost their jobs because of their sexuality or their perceived inability to fit in.

In the midst of this climate of paranoia and despair, Jothams has found a release of sorts in her writing. At Femrite, she has attended creative writing workshops and has been inspired to produce several short stories. She has ambitions to write a novel about her experiences, "so that people can understand", but, as yet, her work remains on her laptop – unpublished and unread by others. In the current climate, no one – not even Femrite – will print her words. It is too dangerous; the risk of reprisal is too high.

Yet the act of writing, Jothams says, is its own form of rebellion. It is necessary for her to put her story down, to show that it exists and to document what is happening. "I feel if you don't tell those stories, you are partly to blame," she explains. "We need to keep writing so that, some day, people will know the truth."

It is a gradual process but, word by word, these women are breaking through Uganda's voice of silence and making their own stories heard.