This coughing is crazy

So I've had asthma for awhile - was diagnosed 2 yrs ago. Did fine on Serevent and albuterol until last winter. Suffered through winter. When warm weather started, things were fine. Now the weather has changed, and I caught a cold, that I am just now getting over. My asthma got fairly bad (for me) from the weather changing, and the cold I caught. I went to the doctor two days ago and he put me on Advair 250/50. The chest tightness is gone - Yay!
But that horrible tickle right at the back of my throat is worse - you know, that tickle that makes you cough until you're gagging and your eyes are watering and your cough has that high-pitched wheezing sound to it?! I used to only get that kind of cough occasionally, now its happening several times a day since yesterday (when I started the Advair). Could this be from the Advair? From the cold I caught? Or the asthma getting worse?