What Other Available Solutions Out There for My Cough?

Question

I am 40 years old. About three months ago, I was down with a cold and suffered from severe cough. The cold went away but the cough remained. So after three months of dry cough, I went to a doctor and I was diagnosed with asthma. My cough is always dry and occasionally productive. Now, I am on a prescription of Advir, Maxair, Claritin and Singulair. I generally don’t have any problems at night and have good sleep every night. Also, I don’t smoke. I have been frequenting doctors and they have been prescribing antibiotics for sinus infection and prednisone for inflammation. If anyone has any more valuable insights please drop in.