unfortunately, there is only so much we can tell you without having the snake in front of us.
Even a vet couldn't tell you that much, say...over the phone with this description.
if infact the interior of the mouth did get "scratched" by say a rodents teeth, nails, etc... which seems like something that very well could happen, then feeding it still is not going to help it. you would only be opening the wound more, if the snake was forced to stretch its mouth open to swollow prey.
So i would cease anymore feeding till you figure out whats causing the swelling.
it could very well be an abscess.
Which are usually caused by a secondary bacterial infection "usually" due to bad husbandry and unsanitary conditions.
Now im not doubting your husbandry here, but things like spot cleaning substrate, long intervals between water changes, water bowls on/under heating elements, water bowls just rinsed and refilled, rather then scrubbed with soap twice a week, same with enclosures/rubbermaids, temps too high/low, are all things that can turn a simple scratch/wound into something much more serious.
You cant see bacteria, and even when husbandry is percieved as top-notch, these organisms can and will grow.
Chances are, if it is a secondary infection of gram-negative bacteria, it probably came from the water, seeing that its internal. it could be as easy as travelling through feces/urine and tracking it into the water then drinking it.
Im not sure how your keeping it, but id advise you to keep it in something like a rubbermaid (easily cleaned), with very good ventilation (hot humid environments help bacteria grow), plastic or no hide, paper towel substrate, and a ceramic/plastic water bowl.
All of this changed and scrubbed daily till your done whatever treatments and things are all healed up.
you'll obviously want to get a bacteria culture, sensitivity test, and the aid of a vet to check inside the mouth for starters. the fact that it sounds like its "spreading" down the vertebrea is what is scaring me, as a smaller more "simple" abscess would be somewhat easier to contain and extract the inflammatory debris.
Im hoping you have a very good vet, because it seems like you might need some sort of anesthetic surgery if antibiotics and treatments dont work.
goodluck!
grant vg