Heh, that was the first symptom that got me on my very long road to diagnosis. I would cough after strenuous exercise and sex. But that was it. I didn't smoke or engage in anything that should cause a cough, I was young, etc. Took a looong time before I finally saw a pulmonologist who could recognize bronchiectasis on a CT, which I apparently had already had for years at that point. Bronchiectasis, in relatively young people, is almost exclusively caused by cystic fibrosis, so that got the ball rolling on the long path to diagnosis.

Some doctors may not like to know that they are your second opinion or third opinion, but it kind of saved me continuing to go to different doctors.

Not to say that you have anything so serious. It's extremely unlikely that you do. In fact, the most common cause of a mysterious cough is post nasal drip, if I recall correctly. I just think that people are less aware of these sorts of possibilities than they ought to be. I literally laughed when my pulmonologist first suggested I might have CF.

Edit: to be a little more helpful, you might want to try something like an Aerobika flutter device and/or a nebulizer (you'd need a prescription). They're good for helping to clear out the lungs, and you don't need to have some sort of special condition to use them.