Whether this infection started off as a temporal gland infection or some sort of injury to his gum is hard to tell from the pics. FYI, jax have a gland at the corner of their mouth that can get impacted and abscess. Herp abscesses don't drain on their own as the material isn't liquid...more like cheese. Just why jax are prone to this isn't all that clear, but it could be related to some sort of nutritional deficiency. Anyway, they probably get started when the cham's immune system is run down or overwhelmed by some other problem. The original infection can spread and they can be tough to eradicate. These infections can also spread to the sinuses if left untreated, so you do need a vet. Usually they will have to probe and clean out any abscess material AND give the cham some oral antibiotics to get at the bacteria lurking out of reach.
From your pics it looks like the infected area isn't right at the gland, but without seeing inside his mouth hard to be sure. These are painful and the cham may be reluctant to eat or drink just when it's so important.