should check stop taking the medicine for a couple of days 2-3 dyas and see if its the meds or an underlying causal agent like asthma or pneumonia chest infection .get diaphragm check .when you cough what colour sputum are you cringing up .if white frothy to clear then its not an infection if brown yellow and or bloody then it is an infection and go back and get a sputum culture of that infection.
I would chat to your doctor about the cough before taking yourself off the meds and also check and look up mims and see what the contraindications of the medicine you are on is