Is there a way to get an apartment for free?

[RPanic04]

My condition is so severe that I just can't function unless I'm extremely tanked up on benzos. The only way I figure I can work is by taking some 4-5mg of xanax per day (this is NOT due to tolerance, this was my initial dose needed from the start years ago, anything less doesn't do a thing, even this just somewhat calms me).

I'm 24 and staying at home, I desperately need out. My mother is a huge aggravation to my panic, she's an extremely unstable, cold person. I've had this for four years, been on every med, had every test, the doctors say there's literally nothing left for me.... my mother just gets pissed off and says that i'm going to drive her to the grave because of my "stupid illness" and that she shouldn't have to put up with it. Basically all she does is put me down for having this, which is cool, she was always like that... as a child she would always yell at me when I had a flu or cold, claiming it was my fault. She goes through weird moods and is just a person that will drain all the positive out of you. Needless to say I need out ASAP, unfortunately my illness is making work very hard.

My plan is this, I can't take xanax daily b/c it starts to lose it's effectiveness fast, however if I take breaks during the week it helps a lot.
I figure my way out is to find a job where I can work three non-consecutive days a week, about 24 hours a week, that way I can get some work in and also have days off from the benzos. If I really cut back on costs this covers EVERYTHING I need except rent.....

Which leads to my question, in the U.S. is there any way to get a free place to live? All I need is a 300-400 sq foot room with a fridge and a bathroom, I don't even need a stove, don't need furniture, don't need any bells or whistles. I'm literally just going to stick my home gym in there (workout nut) and a blanket on the floor to sleep on..... I'd be a million times happier living like that then living in a big house like I am now with someone who does nothing but insult me, throw angry fits and puts me down.