Why wont my cough go away?

I got a bad cold march 24-28 with soare muscles, cough, weakness, fatigue, nasal congestion....no biggie but a pain. Its now April 5 and im all better but all that remains is this deep cough. I dont have a fever so i dont think its pneumonia... maybe bronchitis or asthma? Its like im fine for a few hours and then randomly i will start coughig hard and persistantly for a period of time then im fine again. i cough so hard it hurts my head and i get terrible headaches. Whats wrong with me? i dont want to go to the docs for a stupid cough and im way too busy right now so im asking for your advice