Dry Barky cough for 5 weeks throat pain.

Hello Doctors, My 14 year old son is coughing more than five weeks. He had cough and strep throat initially and finished amoxicillin antibiotics. Cough didn't go away after the antibiotics. Did chest X-ray and found all clear. No sign of wheezing. Later they said he has minor ear infection. Now on Amoxicillin clavunate. It's almost 8 days after new antibiotics . He still have cough without mucus with loud noise. He coughs a lot in the morning until lunch time. He get few hours break after that. Again from 5 he starts cough until 1 am midnight. His cough is loud without any mucus. He is getting constant throat pain due to cough . What are the diagnosis we should do at this stage? I did only X ray. Is there any other tests we can do to figure out what's causing these cough? It's making him miss too many school days loosing sleep. I am badly in need of some expert advise on what can be done. Thanks Anitha