We can't diagnose here so I can't guess what you have. But if it were me my order of actions would be
1) see pharmacist and/or GP for advice
2) try gargling/rinsing mouth with salt water to see if that helps?
3) I wouldn't assume that this is necessarily a diabetic complication, though I'd also do my due diligence and check whether any new or old meds I was on have this as a listed complication. And obviously, if my bgs were consistently high, I'd mention this to GP/pharmacist as a possible contributory factor.
Good luck. I hope you get some relief soon.