Is the skin that's coming off hard like a scab? Is it skinned down to the tissue or bone? If its hard like a scab, it probably is and you should just have to keep it clean and apply an antibiotic ointment., If its down to the tissue or bone, it could be more serious. However, the first thing I would do it check to make sure nothing has gotten wrapped around his lower jaw and has cut off the blood flow. Remove the culprit if you find one. Otherwise, try keeping it clean and apply the antibiotic cream.
You might also try to contact the Humane Society for a referral or try googling for cat associations about helping with your vet. bill.
I understand how you feel about the high costs of care. I think one of the best things I ever did was work for a vet for 13 years. Maybe your vet would let you 'work it off' but cleaning cages, bathing dogs etc. It can't hurt to ask.
Can you just call the vet and describe what you see (not bleeding, size, location etc.) as well as to mention your cats current temprement? Generally when something is wrong with an animal one of the first things you'll notice is a change in your cats' normal behavior, as well as appetite. I know with my Vet I can call with concerns and usually (unless it's serious) they provide me with things to do/look for and generally recommend I call back if the issue worsens, or isn't getting better. Also if you Google "help with Vet Bill" or something similar you can find a wealth of information. Also I recently came across a posting in here that had a link to several organizations designed to specifically provide assistance to individuals in need. Good Luck!
It sounds like it might just be a scab of dead skin from a scratch. Examine it and if it is not red or bleeding or swollen at all, it may not be a problem. If there is any kind of open wound, try putting a little antibiotic ointment on it to keep it from getting infected.
Here in the UK we have vets who help pets of people on benefits, and with little money. We just give a donation that we can afford. It is called the PDSA. (People's Dispensary For Sick Animals).
I don't know where you live, but is there nothing like that near you like that? I can understand you not wanting to pay vets bills. I would put it on a credit card, and worry about it later. You have to get your cat looked at.