Cough got so many possible causes

The first you want to identify is whether its a dry/wet cough. Dry cough means no coloured phlegm, normally due to irritation (e.g. post nasal drip). Wet cough got colored phlegm, which means caused by infection and normally means got infection in lungs.

Just go to doctor to get it properly diagnosed. Using the wrong medication for the wrong cause of cough can make things worse.