In reply to toasted:
I've suspected I've had mild asthma for years. Asthma runs in my family (my Dad had it bad and my brother developed it as an adult) and I've always had a persistent cough. Very occassionally I'll get a bit wheezy after a cold weather very intense run (e.g. intervals).
I went to the doc and explained all this and she asked me a few more questions, but was not particularly concerned there was anything else going on, said the persistent cough could be either mild asthma or acid reflux. To see if it would help, she readily prescribed a preventative inhaler (salbutamol I think). I got the feeling if I'd gone back for more having said it worked, it would have been quite easy to get a repeat prescription.
Anyway, I used it for a while (couple of puffs before a run) and, perhaps it was all in my head, but it felt like it may have helped. The inhaler ran out some time ago and I haven't been back for more, mainly because it wasn't a dramatic improvement and I rarely experienced noticeable difficulties anyway. I did notice (when resting/lying in bed) I got some "palpitations" whilst I was taking it which was listed as a potential, but not worrying, side effect.
Summary: go see the doc and explain everything...including your suspicion it might be exercise induced asthma. Nothing to lose really.