Exercise induced asthma is more common is childhood/adolescence but can present at older ages.
A good test is a methacoline/histamine challenge - bronchoprovocation where we try to elicit a 20% drop in airflow. If we can't provoke that, you don't have current asthma. If you don't have asthma, you don't have exercise induced asthma. A positive test doesn't prove asthma, a negative test excludes it. Easier than an exercise challenge, though sometimes those are also done. If you're well insured you can even talk yourself into a free V02 Max cardiopulmonary test

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A trial of medication can be useful if testing not done. EIA (exercise induced asthma) almost always improves with the use of a bronchodilator (e.g. Ventolin) pre-exercise, if symptoms don't it's probably not EIA.
Bronchodilators pre-exercise work well, especially long-acting ones if you exercise beyond a couple of hours (e.g. Serevent, Oxexe). Anti-leukotriene drugs e.g Singulair also work well esp if you need something regular. If asthma symptoms present at other times also (which is often the case even if not recognized initially) then inhaled steroid meds or combinations are usually indicated (e.g. Flovent, Pulmicort, Advair, Symbicort).
Cheers
General comments only, not personal medical advice.