I had a veiled with this in the 1990's. The veil side of mouth, and at the end even the eye sockets, swelled, just like OP. The cham was 6 years old and this had slowly been building over 90 days. I decided to put him down vs trying to squeeze out another set of "months" with no real quality of life. After he was gone, the vet said the jaw was impossible to open. I did not pay for an autopsy or blood work.
This was in the dark ages, so it had nothing to do with too much lighting or to high of D3 (i use stick tongue farms). Im guessing it was a vit A deficiency that causes an infection in the sinus, which caused a blockage, which seized up everything.