If it's not a bad case of mouth rot it's treated with betadyne being put on the infected area with a qtip. It's a little easier said then done. Do you see actual sores in the mouth? I had a rescue a few years back that had the wood chips stuck in its mouth and that's what was causing the irritation. Mouth rot can be a serious issue depending on how long this has been going on and I really suggest taking him to the vet just to have a professional look at it. You also need to establish how severe the mouth rot is. Mouth rot can quickly start secondary issues so you may need to find out is antibiotics are necessary. The symptoms you are talking about does indeed suggest mouth rot. Although you wouldn't really see puss drain out bc reptile puss is actually cheesy like. Yucky stuff.
Anyways for now you can get a bottle of betadyne from any drug store and put it on the affected parts with a qtip. ( you should always have a bottle of betadyne handy anyways) You may need someone to help bc he isn't going to like that at all. Do this 2x daily, and if it's not a bad case it will get better. If it doesn't look like it's getting better a vet trip is in order!
Morgan