However did I end up in this place with so few resources? The local hospital is losing its dialysis facility, which means dialysis patients will have to travel at least 30 minutes 1 way, three times a week, for treatment.
That sucks. But it does help put things in perspective.
I agree with the folks suggesting you leave an old, recently worn, t shirt and food on your front step. She'll probably come back within a couple days.
Cats can be cared for cheap, at least in the short term. Store brand dry cat food will keep them going just fine and is very inexpensive if you buy the big bags. As is the old non clumping type clay cat litter. Alternatively, I know some uber environmentalist folks that use shredded newspaper for litter, and you can probably find a free source of that. No so good on the odor control, but it will keep them going in the short term.
One other idea...while caging cats is somewhat unorthodox, it can be done, and would be better than having to put her down. Perhaps you can find one through a freecycle group/craigslist/something along those lines? Perhaps one intended for a ferret? They seem to be fairly large. That way you could just let her out when you're there to supervise and keep an eye on her butt.
At the risk of repeating myself, you are stronger than you give yourself credit for and you will pull through. Just take it one day at a time.