I can't imagine the stress you are going through.

Question: don't you have an MI dx that maybe you could use to get a social worker and get help getting into one of these shelters?

I think it's smart to just realize that you may have a few nights to spend in your car and figuring out how to do that safely. I do think that it's important to continue the search for a room for rent or roommates (which would require less of a proof of income - on this note, when I was in grad school my tuition refund statement was enough to prove proof of income; can you use that or ask if you can use that? Have you asked to use that to show your proof of income for the semester?)...continue the search for a room for rent or a roommate situation so that your time in your car or at a cheap motel is limited.

On another note, I know work options are somewhat limited, have you tried any freelancing sites for quick writing or copyediting/proof reading jobs, etc? You won't make same day cash but you will earn some money and that's something. As you continue it can grow into some substantial earnings. My suggestions are Thumbtack or UpWork. There are other sites but I've heard there of lesser quality. Don't know if you already tried this but wanted to suggest it. There are people who need academic help on those sites, like checking their homework, etc. Again, it might not be a lot to start but it could help and get you started somewhere. Could also get you some quick references...

With two weeks left in your apartment, I do hope that you will take a few minutes each day to soothe yourself and allow yourself a calming space to sort of save up for the stress that's to come. Even if it's just a few minutes of sitting still with deep breaths, as I can tell you are feeling the current and impending stress very acutely. I want you to know that I think often throughout the day if there are any ideas I can send your way. Know that we all care and want to help in whatever way we are able.

Seesaw