Advair without Asthma or COPD

I have had a horrible and painful cough for longer than 3 weeks that is getting worse. It is dry and bark-like. My doctor has prescribed me advair for only 3 weeks. She swabbed my troat and listened to my chest and found no sign of bacterial or viral infection. Her explanation to me is that I have inflammation in the lungs and trachea. Probably from oversensitivity from the strep throat I had 3 months ago. She said that because I was sick I am more sensitive to the smoke in my workplace and that it has built up so that now have coughing fits. I was doing a lot of research on advair and my question is - Will advair help me even though I do NOT have asthma or COPD? I can find no evidence that it does help so is it just a waste of time and money? I have been tested in the past for asthma and have been told that there is no way I can have it. Is it healthy to be taking a steroid inhaler? My prescription is advair 250/50 2 times a day for 7 days and then one time a day at bed time for an additional 14 days