What do you do if antibiotics and flonase (both prescribed for sinus infection) do not cure the infection and it doesn't go away?

CT sinus: If it is indeed a sinus infection which fails to respond to antibiotic, then one must determine first whether the abx is the right one. For example zpak is not great on sinusitis. A ct scan of the sinus would detect obstruction of sinus drainage or allergic fungal sinusitis. See an ENT if necessary.

Call PCP: All antibiotics have a statistical rate of failure that may approach 10%. Sometimes a second round of a different antibiotic must be used for sucess. There is also the possibility that the first diagnosis was in error and other issues caused the symptoms involved. Call your pcp and discuss your symptoms to see what alternatives you can have.