That is really more of a collection of lung conditions where the lungs are too reactive to harmless substances. It is important to rule out other reactive airway issues to get the propper
treatment. There are other conditions that cause broncho-constriction besides asthma.
Either way though, with your reactions after exercise, it sounds like a fast acting broncho dilater (some form of albuterol - Proventil, Porair, Maxair, Xopenex, Ventolin) might be a good idea.