Sulmet will work for coryza, but you may be dealing with something else here. Is there a foul smell coming from her, particularly from her nasal disharge? If not, I would start treating for mycoplasma. Tylan is a good bet, because it treats both coryza and mycoplasma. Tetracycline will work for just mycoplasma as will Denagard.
The trouble you're going to run into here is that a law just passed that prohibits the sale of a lot of medicine that goes in water OTC. Tetracycline and Tylan are some of the meds affected. You may still be able to get injectable Tylan OTC but for the rest you will need to go to a vet. Denagard is still available to purchase OTC as it is not affected by the new law.
It could also be some sort of virus, like infectious bronchitis, that just needs to pass on its own. If that's the case, antibiotics are not going to help.
Please note that if it is coryza or mycoplasma, she is going to carry it for the rest of her life and pass it to other birds that she comes into contact with.
