Yep, that's a pretty nasty infection going on there. Chams are tough and try not to react to a problem so they don't appear vulnerable to a predator (that's why he's eating and behaving "normally"
. You will definitely need a vet to open this up. As kinyonga said, the infection could be systemic now and the vet will need to do a sensitivity test to determine what antibiotic will be effective. Many vets just default to using Baytril without doing a sensitivity culture but Baytril can be very tough on kidneys. A better vet will clean the thing out, start a topical antiseptic/antibiotic, while the culture is processing, possibly start a milder broad spectrum antibiotic until the culture results come in, then start the most appropriate treatment. Treating it with a surface antibiotic alone won't do it at this point. Until you can get to a vet you could gently scrub it with Betadine and put some Polysporin on anything that looks like an open sore, but it may only slow the infection down a little and ease the pain. It's got to hurt!