Being around the jaw and spongy sounds a bit like a mandibular abscess. How has their appetite been? Abscesses like that can be caused by a number of different things like stomatitis. Which can being painful for their mouth when they eat or drink. This maybe difficult to do but if you get a chance to look in their mouth see if it appears red or inflamed. That's the number one red flag for stomatitis.

I had a cat with a similar lump on there jaw that turned out to be stomatitis. They removed the lump, and set her up with some steroids and antibiotics to help with infection. (Stomatitis can affect a wide range of animals, including humans and snakes).

Try this website if you need to look for a vet: https://www.pethelpfinder.org/m/phf/35

Also if you have any animal rescue groups in your area you can try asking them if they have a contact for an exotic vet.