Asthma is a heated debate in the diving medicine arena. Some say don't dive at all, and others say it depends. This depends is based on what triggers a reaction. Some people have an attack with cold, dry air or upon exertion (exercise induced), two elements that can not be escaped in scuba. If you have been diving without complications, then there shouldn't be any reason why you can not become a professional. I am assuming by professional you mean becoming a divemaster/divecon or instructor. I agree with nobends: you really need to discuss the issue with your doctor and call the Divers Alert Network (www.diversalertnetwork.com) and talk to one of their physicians. DAN wrote an article this past year on the very issue of asthma and diving; you maybe able to get a copy of that article from them if you ask (especially if you're a member).
Good luck in attaining your goals.