First things first: How old are you? If you're still in your teens, a lot of that can go away with time. Having suffered from chronic asthma attacks myself (and the occasional bout from time-to-time), I know about it from personal experience. I also know that staying away from physical exercise makes it a lot harder as time goes on. Regardless, get yourself some cardio going, as teaching your body how to utilize the oxygen it needs on a more efficient basis is the best thing for you.
Secondly: Are you seeing a doctor right now? The reason being is this: When I was back in grade school, a lot of the medication that they have currently (even the treatment approaches that are popular now) was not available. A lot of the meds were there to help after the fact that you're suffering from an asthma attack. However, with a lot of the newer meds like Singulair, Advair (and the like) are great treatments for maintaining your body's everyday operation. Instead of treating an asthma attack when it comes full force, a lot of the treatment plans appraoch it by helping your body along so that it is less prone to fall into that situation. If you are dedicated to the idea of training in anything for an extended period of time, consult a physician and let them do what they can to help you out.
When I was in the 9th and 10th grade I wrestled, but didn't ever get to the point where I was truly competitive as I would have liked. Currently, I know that if I take a few months to train ardently, I could get back to the point where I could roll hard for 20 minutes before having to take a break. I still see my doctor on a regular basis, and they all tell me to get into the gym to loose some weight regardless of how my asthma is.
My point: Don't be afraid. But don't be stupid. You can't realisticly expect to jump into a championship UFC match right off the bat, neither should you begin training like you're headed for one. Moderation is key, and is a great way to get yourself acclaimated to anything regardless of the type of activity. I don't think any coach or trainer anywhere will knock you for having to bring in an inhaler with you either.
It doesn't matter if you agree or disagree
... As long as I don't bore you and I spark a moment of thought, my goal is achieved
Queng leon queng tigre ecu tacacut, queca pa? - Pampangan Mandarigma Motto