The Advair™ Diskus® (fluticasone/salmeterol) is not likely to be the cause of the coughing, but might be related to the weight gain. This is a pretty good dose for a 6-year-old. The cause of the cough might be a sinus infection, which, indeed, might take a while on antibiotics to clear up. If the cough is not getting better, I would suggest getting back to the specialist who might start the prednisone again and also check to see if a sinus infection is the cause.
If the symptoms do clear up, you might discuss the weight gain with her doctor.
I was on Singulair - but I stopped it after two years because I was getting pains in my jaw and an unusual feeling of being ill.
Maybe you could see a respiratory nurse, her condition may not be specifically suited to her treatment, there are other drugs out there that maybe would suit her better. Advair is a combination drug maybe she doesn't need that at 6 years of age?
I would ask for her condition to be more closely monitored.
A series of PFT's would show whether the drug was helping or not.
J