I've not had Advair but sounds similar to my Spiriva. I was told it would take a week to kick in properly, now I'm on one inhalation a day plus other meds.
Do get checked out. As Sherry says; it could be just a bug.
Anyway, I empathise. Having busted ribs a few times due to coughing, I am very careful about coughing. If I feel the need, I lean into a big cushion to take the stress off the ribcage and lungs. Not very elegant, but it helps. And don't your shoulders ache too?
Chocolate and/or honey sometimes helps calm things down. I've not found a cough medicine that does any good so far.
I hope things improve for you.
Jesus Saves - Buddha makes incremental backups