Kennel cough- am I out of the woods?

Adopted a 5 month old pup from the SPCA on the 8th of July, upon bringing her home we found out she had kennel cough. Took her to the vet after 2 days of seeing no improvement (she'd cough all day and all through the night) . Its been 2 days since she finished her medication, and the cough has definitely improved. However she does still cough the odd time, now it sounds more wet like she is trying to cough something up rather than just dry hacking. She coughed up some phlegm today, which is the first time she's done that through the entire sickness. She also doesn't seem to be eating all of her food, but that may have something to do with her not really liking her kibble (I have to mix it with a wet food I bought from the vet before she'll even sniff it.) I suppose I'm just wondering if this all sounds normal and if I should continue to believe she's on her way to being a healthy pup?