How Can Chronic Cough Be Treated?

I was diagnosed with pneumonia nov. 13th after being diagnosed with chronic sinusitis/bronchitis about two weeks before. First I took Zpack and prednisone, then with the pneumonia took a different antibiotic doxycycline. Up until the day after Thanksgiving, by following the doxycycline doses, I felt much better. But now the cough is back - unproductive, sudden, makes my asthma bad. It starts as a feeling in the back of my throat (probably from post nasal drip) and it triggers coughing. No yellow or green gunk, just spittle that is clear. When I cough kind of like I am gagging, then it makes it go away.