While your guess at asthma is a good one, I'd want to eliminate any cardiac-related causes first, such as some sort of structural abnormality. While this seems relatively unlikely, especially since you've had the problem since you were 10, it would make sense to have this ruled out first -- unless that's already been done.
So let's assume you've ruled out (or will rule out) any sort of congenital structural abnormality of the heart. That would likely leave exertionally-induced asthma as the likely culprit. This usually (but not always) occurs secondary to gastroesophgeal reflux disease (GERD), and exercise seems to cause a flowover of gastric juices, which are aspirated (it also happens at night quite often, during sleep), irritating the bronchi and resulting in shortness of breath after brief exertion. Basketball would be good for that for sure.
But first I'd try and have an echocardiogram done, just to be certain there's not something (it would most likely be a malfunctioning valve) going on with your heart. Quite possibly, given the right primary caregiver, you could get this all done at once.
I hope this is helpful to you and that you'll follow up with us if you have any further information, antything new comes up, or when you have an exam to determine what may be causing this problem. Best of luck to you.
John Kenyon, EMT, CCT
Non-invasive cardiology tech, Emergency and Critical Care technician, Critical Incident Stress Mgmt. specialist