Can it affect you? Yes, it definitely can. Will it? Probably, at some point it will. How much depends on numerous factors. First, what type of asthma do you have? Allergy influenced asthma doesn't affect athletes as much as exercise-induced asthma. With EIA the cause of the inflammation in your lungs is the exercise you are doing. The effects can be mitigated by proper control through medication and awareness of your body and outside influences that make it worse when you exercise, for instance, temperature and humidity. There are also studies which suggest that a lack of proper hydration can increase the liklihood of an attack.
The best thing to do is to monitor yourself and your symptoms so you can tell your doctor exactly what is going on when you notice you have a problem. This way he/she can tailor your treatment specifically for you. As an asthmatic, I can tell you that you definitely need to see an asthma/allergy specialist and not just a general practitioner.
Lots of high level athletes have asthma. Yes, sports like wrestling, competitive jiu-jitsu, etc are more difficult on asthmatics than distance sports but don't let that deter you!