Hi,
For some reason there is a corrolation between childhood eczema and a later development of asthma. Adult onset asthma can also develop from untreated/controlled allergies, result from a viral infection (bad cold), chemical exposures (work and household), poor air quality where you live.... There a many other possible non-genetic reasons that one can develop asthma older in life. Sometimes it isn't that the patient developed asthma as an adult, it is that their asthma progressed to a point that the require treatment but had it their entire life.
As the other poster said, it can be genetic as well as environmental. It is verily well documented that children who grow up around smoking are much more likely to have/develop asthma at some point in their lives than those who have lower exposure levels to cigarette smoke.
FYI - A sterile invironment is really bad if you want a strong immune system. A strong immune system means that your body knows how to make antibodies to fight pathogens. Your body "learns" to make antibodies only after exposure to a specific pathogen. That is the reason childhood immunizations are effective. A small controlled exposure to mumps, measles, chicken pox, polio.... teaches the body how to make the antibodies so that when the body is exposed to the virus in the real world the immune system can go to work fighting the pathogen immediately keeping you from getting sick. That is also why yearly flu vaccines are effective. However, flu viruses do tend to mutate so what is effective one year is probably not going to be effective the next year.
God bless.
Eczema is a topical reaction to an allergen. For me it caused by touching perfume; for others it could be from diet. Asthma is a reaction that restricts the lungs' ability to work. This can be caused from an allergen as well, but it can also be caused by environment. (My grandma isn't allergic to cigarette smoke but if she walked through a cloud of it she might have a hard time breathing.) So having the two in your history may mean you have an allergy you are unaware of, but you can easily have one without the other.
Why you're the only one with it, that's kind of hard to say. Some immunology is definitely genetic, but a lot of it seems to be environmental. My best friend is allergic to over 20 things, her mother is only allergic to red wine. I've been allergic to perfume since I was 2 weeks old, my mother is only now (at 50) starting to get migraines from it. I've read a few case studies that suggest that the environment you grow up in may make you more likely to have asthma and allergies. Such as if you have siblings no older than 5 years your senior living with you, you are less likely to have autoimmune problems and allergies. Another study showed that children who grow up in 3rd world conditions are less likely to have autoimmune problems then children growing up in a sterile environment. I don't remember where exactly these studies were published but I'm sure you'd be able to find them if you search around peer review scientific articles. Unfortunately for the most part immunology is still a growing field, muddled with uncertainty. Right now all you can do is deal with what you have.
I suggest you see an allergist and perhaps get tested for the most common allergens. Also it might be a good idea to stop smoking (if you do), loose weight (if you've got any extra lbs), and look into air filters.