It sounds like your daughter is under medical care- with your description & the fact she has an albuterol inhaler. If not, persistent coughs should be checked out to rule out something more serious. Even then, sometimes coughs linger with no real explanation.
Here's a trick we use here with surprisingly good success: Dab a LITTLE Vick's VapoRub on the soles of each foot, it doesn't take much at all, cover loosely with socks to prevent staining & slipping.
I can't explain why it works, just that I was at my wits end a few years ago with several hacking coughers, including me, and decided it wouldn't hurt to try it, even though it seemed ridiculous. It worked! Now whenever we're all in bed at night and hear a hacky cough, my husband gets the Vick's and quiets it down.
Just a word of caution: Vick's VapoRub contains camphor, which can be quite toxic to children- so remember to store it properly. Even though it would taste bad to an adult, small children often put things we wouldn't in their mouths.
Please let me know if you try it and it helps (or even if it doesn't).