I'm not sure of any ways to treat Mastitis other than with an antibiotic. Mastitis is an infection of the breast tissue, and usually you should get that treated as soon as you seen any signs.
I had mastitis with my 2nd child and was able to call up my ob and they were able to call in a prescription for me without having to have an office visit. I remember the chills like they were yesterday - not fun! I always had to try to keep up with the feedings, and even when my daughter slept through the night more, I still woke her up to nurse to prevent this from happening again.
Can you find any free or low cost clinics in your area? If not, then maybe you can call up your ob-gyn that you recently delivered with, see what they say, and maybe you can work out some kind of payment plan with them. Also ask if they have any antibiotic samples that they can give to you (free).