I have tried to heal the sore with Neosporin, peroxide, and a saline rinse. It just won't heal. Do you have any advice as to what may speed up the healing for this?

No. We can't help you with that. We know nothing about your medical history and we do,not diagnose here. See your doctor. A sore that will not heal near internal membranes is serious.

I agree with tickle... stuff like this is a red flag its time to visit a doctor.