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How ol is you cat?
has she taken any oral antibiotics?
if so, which ones and for how long?
is she eating?
Please stand by while I type detailed answer.
About how large is the wound?
This can be caused by a dental issue. An abscessed tooth or root in the gum or a frature to a tooth. Any of these would send bacteria into her system an cause a wound to stay open.
She may also have a weakened immune system due to a kitty disease.
Any infection must be treated by a broad spectrum antibiotic like Clavamox or clindamycin and for enough time to distroy all bacterium. Otherwise it will reflourish (stronger than ever) and reinfect her soon after the meds are stopped. Doxy is not the proper script for such an established infection.
In the meantime open a Vitamin E capsule twice a day and pain the lesion with it. Apply almost hot compresses to bring the infection to the surface and then neosporen all three times a day.
To boost her immune system add a quarter teaspoon of colloidal silver to her water daily. It is safe for the other cats to drink it:
Please let me know how she is doing. If you have more questions, I will always be here for you.
Sincerest best wishes,