I agree with the others on the fact that you may need to distance yourself from, if not cut yourself out entirely, from your family. If you're not being supported by them, then I don't think that's what one would call an unconditional love. It sounds like your mother's constantly abusing you emotionally, and you should get yourself out as fast as you can.
I know it's easier said than done.
I was kicked out when I was 19 (I'll be 24 in September) because I finally stood up to my abusive father, so I know speaking up for yourself and being intense about how you're the one in the right can cause some serious backlash. I was lucky, though, and two of my close friends helped me and I had a job already, but I sent over 300 applications to get a second one to support myself and only heard back from 2 places. I understand it's difficult.
I was wondering if you could look for someone looking for roommates? If you were looking at graduate school - I'm not sure if your university does this - but usually grad students here have their housing and expenses taken care of through grants/scholarships, usually. Either way, University's usually have people in houses or apartments that need roommates as others graduate or leave, so that could be something you could look into; that's what I ended up doing. I know Delaware is a far cry from New York, but I managed to find a house with 3 bedrooms that was $1k and live with two wonderful people now who've been nothing but supportive (I mean, it's in the ghetto (which isn't the same as where you're from I'm sure), but you gotta do what you gotta do). You could be able to find something like that, maybe? A house/apartment with a bunch of students?
As for not being able to finance it/find a job in time...have you thought about getting a gofundme? That's what I was using when I had issues with my Financial Aid for school. You can use it to raise money for personal reasons (it's like Kickstarter but better imo), so perhaps find out how much rent/deposit would be for the first month in an apartment on your own and continue applying for jobs (my roommate and I have made it a tradition to have a small celebration every time her application mark hits 200...she's having trouble too, and she's a geneticist I promise it's not your fault you can't find anything) while you have the month to get settled in and settled down.
The environment you're in right now is toxic, and that's no good - you need fresh air. Perhaps they'll come around if they have time to mull it over. Especially if they get time to miss you. My family and I aren't on the best terms, but they wanted me to come back after I didn't talk to them for a year (I didn't, but I do occasionally for holidays- mostly because of my mom, so I understand that close bond you're worried about losing).
All the best. I hope things for you improve. Never hesitate to send a PM to me if you need to talk, either.