You really need the vet....even if you posted pics, it's hard to say what's going on here. Seems like some sort of infection but not your typical "mouth rot".
I hope your vet is up for the challenge... Do you feed live??? I got an accidental mouse-bite years ago when I broke up a fight (accidentally got in the way)
and the infection was "impressive" to say the least. When was he fed last?
As far as something stuck in his teeth (or in his gums?), what are you using for substrate? Anything with potential wood splinters?