K.B.
I have a son (4.5 years old) that has asthma and his flare ups are mostly illness induced. Before we knew he had asthma, it would seem like his colds/coughs would last forever. If he had a cold, he might still be coughing 2 weeks after the congestion part of the cold was gone. His fraternal twin brother, on the other hand, would get the cold and have very little coughing.
After he was diagnosed with asthma, we started doing nebulizer treatments with a preventative/maintenance medication. It wasn't Advair, but it was a similar type medicine (budesonide/pulmicort) for kids in nebulizer form. We also have albuterol nebulizer medicine that we give as needed.
Our approach is to give him one treatment a day during the sick season. So this is typically fall/winter, but we tend to do it during the school year. If he shows signs of getting sick, we bump it up to 2-3 times a day for the maintenance medication. In the summer, we stop the treatments unless he gets sick. Only if he has some wheezing or some sudden bad coughing do we give him an albuterol treatment.
If we keep on top of this strategy he has very little, if any coughing at the end of the cold. It is so much better.
In case you are not aware the difference between a maintenance medicine and albuterol is that the maintenance medicine works to prevent or reduce the asthma symptoms from occurring whereas albuterol tries to alleviate the symptoms after the fact. Depending on how severe the symptoms have gotten, battling them back can be difficult.
If you haven't taken your daughter to a pediatric allergist/asthma specialist, I would recommend seeing one.
It's a bit of a hassle having to set aside time for nebulizer treatments, but the quality of life improvement in my son has been worth it. We also have a rescue inhaler (albuterol) we take with us when we are out and about just in case, but it's rare that we actually need it. When he gets older, he will do his preventative medicine in a puffer/inhaler as well, but for now we feel the nebulizer treatments ensure he actually gets the medicine in his lungs.