It is 13 years since my son was born. His due date was 29 February, but he waited until the clock had tipped safely into March, guaranteeing him annual birthday parties. In the delivery room, the midwife whisked him off to be checked over: he was a good size, a healthy colour and had fully functioning lungs judging from the enthusiastic crying – but his hands were unusual. Several fingers were joined together. They looked just like perfect baby fingers, with tiny nails and creases, but were stuck together like the pages of a book that hadn’t been cut. The midwife, putting on a cheery voice, said that webbing was traditionally a sign of good luck. But the paediatricians were less fanciful. The doctors who looked him over didn’t look at us; they talked to each other out of our earshot, and then suggested referrals to a plastic surgeon and a geneticist.

When we met the geneticist, she told us that there was one extraordinarily rare disease associated with syndactyly (the medical term for joined fingers). She had read up on it, and judging by the photos of patients in the research papers, she didn’t think our baby had it too. But she told us there was a blood test that would allow us to rule it out. Blood samples were sent to the US. Three months later, the results came back. Our son did have a genetic disease that affected just one in 10 million people; there were only a few hundred known cases in the world.

We were thrown into a series of appointments with specialists who had never seen anyone with this disease before, who hastily read the few available research papers before they met us. They told us our son was healthy, but he should be monitored for the associated problems that might arise. Nothing was certain, as it did not affect everyone in the same way. We searched the internet and I learned a lot of new vocabulary with a medical dictionary by my side.

The research papers came with scary photos of unhappy adults, and one very alarming looking child. I could see why the original geneticist did not think my son had the same disease. These portraits were harshly lit, grim, black-and-white shots. They were like anonymous ID photos from a police lineup. None of them resembled my beautiful boy, with his piercing green eyes, who smiled and waved at strangers with his funny-fingered hands.

At Great Ormond Street children’s hospital, the surgeons took tiny skin grafts from his tummy to stitch between his fingers after they separated them. They did an excellent job and after some more surgery when he was 10, he can now play the piano and type messages on Minecraft. The other specialists we saw were all keen to meet him because his genetic disease is so rare, but what I really wanted was to find someone who had seen this condition before and could tell us what would happen to him as he grew up. I wanted to meet wise experts, not interested observers.

We went to the US when he was two, where there is a geneticist researching his disorder. She had never seen anyone so young with it before. Luckily, one of her older American patients had started a support group, and she put us in touch with him. There was a one-page website, with tiny pictures of a dozen members from America and a few from Europe. We exchanged some emails and it felt good finally not to be alone.

Through the website, we met a friendly English family with four children, whose third son has the same condition. He is a little younger than my boy and when we first exchanged photos, it was startling. They had the same pale, slanting eyes, the same fine, fluffy hair, the same webbed fingers and the same tiny teeth. We got together and found both boys were struggling with speech, but were lively, sociable and full of energy. Later, we met up with a witty engineer from Scandinavia who had developed the disorder’s neurological problems in his 20s, but it hadn’t got in the way of life. He is married, has a great job and two beautiful children. Some of the original group have a lot of medical problems, while others are managing well. The syndrome is very variable in outcome, and it is important to know the important symptoms to check.

When the website’s original founders became too ill to update it, we transferred it to Facebook – and since then we have found many more members. We’ve kept it a closed group – you have to ask to join and explain your interest. We want to share our problems with people who know what it is like living with this condition; we don’t want to attract morbidly curious strangers interested in medical oddities. My son might not want everyone to know that he has a genetic disease when he gets older, which is why I’m not using our real names here, or identifying the condition too precisely. But in the light of Rare Diseases Day, an awareness-raising campaign, I hope that our story will inspire other families living with obscure conditions to find each other online or set up support groups.

The support group on Facebook is international and relatively easy to manage. We can swap information and share what is helping us to manage health problems. But we can also share photos of successes; first day at school, birthday parties and wedding photos. Seeing a little girl in another country proudly demonstrating her karate poses is a much more positive first glimpse of life with this disabling condition than the nightmarish photos I found on the internet 13 years ago.

We have become a far-away family tht keeps in touch in cyberspace. And, like all distant relatives, we have our moments when we get it wrong and upset each other. It’s not just different languages that can separate us. Some of us have very serious problems (seizures, spasticity, sight loss) and concerns about dry skin and sparse hair can seem trivial. And different countries have very different health systems. The northern European members have free or low-cost medical care, while the American members have to convince their insurance companies that they need expensive tests and treatments. Other members live in far poorer countries where there is very little medical help; some have reached adulthood without their fingers being separated.

There are ethical and cultural sensitivities, too, when you are talking to people across the world. Most syndactyly types are autosomal dominant, which means that if you have it, there is a 50-50 chance you will pass it on to your children. Some of our support group have several family members with the condition and there is some evidence that its effects are worse down the generations. A few countries offer genetic screening, allowing parents through IVF not to implant embryos with the condition. Other countries do not allow this because it is not a life-threatening disease. Many of our adult members have had long and mainly healthy lives. They see the condition as a nuisance more than a major problem; others would disagree and prefer not to have another child with it. Some of us are religious, some of us are not – and we have to be sensitive about each other’s views about prenatal screening. Like all families, we occasionally misunderstand each other, but mostly we are happy to have found distant relatives who know what we are going through and not feel so alone.

When my son was diagnosed, I worked out that, statistically, there must be about five people in the UK with his disorder. Due to the wonders of the internet, we now know most of them, at least online. In real life, we meet up regularly with one family; our two boys know the strange long name of their shared condition. We hope that when they grow up, they will stay in touch and feel less alone. The condition does have a subtle impact on how your face develops. When I open a new message asking to join the group, I am often amazed to see a photo of a child on the other side of the world who could be my son’s twin, another funny-fingered family member, reaching out to us across the internet.

• See rarediseaseday.org for activities, support and contact details.