Stress test, but no breathing test?

If you have a friend with asthma, borrow their peak flow meter and test yourself before and during a workout, then if it does appear you have exercise induced asthma, show your doctor the results. If you don't know anyone you can borrow one from, I think you can get one from a drugstore without a prescription - they're only like $25, and a good thing to have around if you have or suspect you have asthma.