I've experienced the coughing that you describe after a hard time trial and sometimes even after a tough club ride when I have been pushing myself to the limit and struggling hard to catch my breath. With me, the coughing sometimes even extends into the next day. I have assumed that it is a symptom of my lungs in poor condition, and the fitter I get, the less coughing I have. I would not see a doctor about it any more than I would see a doctor about sore legs after a hard ride. I have ALWAYS recovered without medication. Of course, if you have asthma, you have asthma and that's something different.