My son used to have the similar problem before, always cough. My relative recommended me to see Wong X Ching in Mongkok, specialist in 耳鼻喉. My son then starts swimming, a year now, he hasn't had cough as much as before.
I myself also got cough for 1+ month early this year, have seen several doctors and got 氣管medicine all the times. I finally see him one time and got recovered. I should have seen him earlier but just too far from my home and keep delaying...