Honestly it looks just like what my chameleon had and still gets. It's from eating and there is no way around it. There are two pockets in their mouth, one on each side where the upper lip and lower lip meet, and food gets stuck in there and turns to puss therefore making it look swollen.
This freaked me out when I saw my chameleon like this but the vet said it was totally normal and you need to delicately squeeze from the back to the front (on their swollen cheek) with a Qtip or your finger like if you were squeezing a tube of toothpaste and where their lips meet is where the toothpaste, or in this case, pus comes out. YOU MUST HAVE THEIR MOUTH OPEN FOR THIS
They don't like having this done to them but it's totally normal, it may even bleed, or make their eye(s) look kinda weird. it's uncomfortable for them but not deadly unless it sits there. The swelling also may get worse but should go down considerably within 24 hours.
My vet gave me Silver something to put on it once the pus is all out but only if you think it's infected.
Really not worth a vet trip ($$$$) unless you're going for something else besides this. In a way it's kind of like their version of wisdom teeth, only it can happen more than once, and it is MUCH easier to deal with.
It's kind of hard to figure out how to keep their mouth open and do this so having a friend help works out.
I'm no vet but I have an EXTREMELY large amount of knowledge with animals of all kinds and I know 20+ vets of all kinds and my personal friend is a chammy vet at the Academy of Sciences in San Francisco and told me this is 100% normal if it's only the mouth area that is affected. Otherwise go to the vet.
If it was my chameleon, I'd take him to the vet, so he can get on the right meds asap. I hope he feels better really soon.
