I had asthma all my life. I played all kinds of sports but still had asthma. 2 months after I began running, my asthma went away (almost 4 years ago) and I haven't had it since. One of the MANY MANY benefits of running, the greatest sport in the world. If you think track is too boring, run nature trails. There's nothing better. There are running groups everywhere. Google to find them in your area or just go hit some trails.
Running is also the least expensive sport. $80 for shoes and that's it.