Okay,......To be quite honest, if it's mouth/jaw is swollen, and it's teeth are falling out, I'd consider that beyond the early stages!
I would also bet money the snake is not eating at ALL during the course of all this either,.......correct?
Anyway, I don't know how big the snake is, but you need to first get a thin, flat piece of plastic or wood that has enough width so that when you get the mouth open, you can turn the object sideways towards the back of the mouth to keep it wedged open so you can work on the mouth. Once you get it "propped" open,...remove ALL the cheesy loose tissue, including any loose teeth. After all this is initially removed, thoroughly rinse the mouth very well with a Peroxide solution that has a bit of Betadine added to it via a small syringe or eye dropper. The betadine also helps "stain" the infected tissue, so you can more easily see what to remove. Hold the snake's head sideways a little while you do the rinsing, this way it will drain out of the mouth and stay out of the glottis(windpipe) at the base of the lower jaw. Clean the mouth well each day if any bad tissue is seen, and treat the inside of the mouth with the solution TWICE a day WITHOUT EXCEPTION!!! After several days, you should start noticing an improvement. But DO NOT stop the treatment, as doing so too early can cause the infectious stomatitis to not quite go away and remain infecting the mouth tissue.
After you are SURE it's mouth is closing properly, and things seem back to normal when you open it's mouth(approx. one and a half-two weeks) depending on severity, then you can stop the treetment, but keep a VERY close eye on this for a while.
When the snake starts feeding again voluntarily, this will be a good sign that things are getting back to normal, and it is getting out of the woods with the infection.
If you follow this to the letter, the snake should make a total recovery. But if not, the infection will get nothing but worse, and the snake will certainly remain not feeding and eventually die in a fairly short order. You can easily save it's life here.
If by some chance, you don't feel up to doing this on a steady basis, I strongly recommend you seek out an experienced reptile vet that is familiar with treating this.
good luck!,...and let us know how things go with the progress.
~Doug
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"Better to be silent and thought a fool, than to open mouth and remove any doubt!"