Well, the Vet should have done a culture. Did he offer to run one?
Until you know what you are fighting, you don't know which meds will work.
Doing nothing is obviously not ideal either.
You need to take her back to the Vet, have them take a sample of the mucus and back of the throat and send it in for a culture. Once you know which germs you are dealing with, he can prescribe the CORRECT antibiotic as well as knowing how long it needs to be given..