Suggest Treatment For Cough And Shortness Of Breath

Hi...I have asthma. I have had a dry cough for the past several weeks. I am on advair 230 mcg 2 puffs 2x/s/day, currently on 40 mg prednisone/day, combivent as needed. I have produced small amounts of light colored phlegm, normally in the morning. I also have lower back discomfort, some small amount of head stuffiness and leg weakness. Also have positive ANA, no autoimmune has been diagnosed to date. Anyway, the cough and shortness of breath are not getting better, even with the prednisone. My GP does not think infection. Any ideas?