Sometimes a hard, deep cough is a sign of asthma. My son had those kind of symptoms at a young age too and for several years they just said he had reactive airways, but finally the doctors said it was asthma. He is now on preventitive inhaler medications and does pretty well for the most part. I would ask your doctor to do a peak flow test. Your child just blows into a tube and it will measure lung capacity and how much air he is able to move. Good luck!