If my cough isn't made better by cough suppressants and goes in bursts that can make me vomit, what can it be?

Prolonged cough: Sometimes a respiratory infection leaves behind an irritable area in the windpipe(trachea) even after the infection itself has cleared. This irritation causes prolonged dry coughing spasms. . If an exam and a chest x-ray don't show any important abnormalities then a stronger cough suppressant with Codeine and cortisone type inhaler heals the irritation.