I have asthma. It's not something that'll keep you from leading a perfectly normal life, if treated - Indeed, depending on various factors it may go into remission so that you'll go months without ever feeling it. I'm having one of those periods right now, in fact, and haven't needed medication for almost half a year, even though I know with near-certainty that the spring pollen-onslaught is going to get it going again.
On that note, environmental factors are what seem to cause it, not genetics. For me, it's cigarette smoke, pollen, and certain levels of cool+damp air, the middle of those presumably because I also have mild allergies. When either of those are around, my asthma will flare up with near certainty, but take them away, and a couple weeks treatment (treatment being inhaling twice a day, no pills, needles or other nastiness) later I can breather almost normally again even before I get my daily doses.
So seriously, don't fret it. It's like the most common condition in the world, and it's treatment is probably the least uncomfortable there is.
PS. I served in the army. And they knew about the asthma too, when they recruited me

Asthma wasn't a problem at any point, since inhalers are small and easy to stash.