I Have A Cough For Now 4 Months, Starts As

I have a cough for now 4 months, starts as a dry cough/tickle in throat and once I start coughing deeper it seems that sinus start draining down back of throat. I have seen a doctor and she put me on an inhaler and allergy medics which has not helped. I went to a ear nose throat doctor and he put me on antibiotic and did a scan of my sinuses and found nothing. I went back to my regular doctor and she did a spirometer test and that showed a mild case of asthma very mind. Also did a chest exray of lungs and that was clear. I am still coughing and it is so forceful at times that I spit up clear phlegm. What do you think I should do?