have your doc stress test you - he or she will put you on a treadmill and make evaluations from there. There is such a thing as stress or exercise induced asthma. Could lead to complications later or you might not be getting as good a workout as you could be - your muscles need oxygen and if you're not getting enough to feed them, you could get more tired quicker.
Could be any number of things. A lot of my friends in the city always got it, most of my friends in the country didn't. I think its just thinning out the mucus in your lungs and you're coughing out some of the accumulated pollution and crap.
Either that, or they just go ta workout too, so they're just slightly raw, hence, you cough.