Help Cassidy not become homeless

Hi there, I'm Cassidy, and I'm about to be homeless. I've just been lost my job, I have no savings, and I have less than a week to find a new place to live. I currently live with my sister, but I've had so many issues trying to keep a steady job that I owe her $1600 in rent from the past few months that I  just haven't had. She's given me until August 4th to move out, and without some serious help I'm going to end up on the street. I'm a mentally ill transgender woman with no job and no source of income and a history of suicidal behavior- being homeless, whether on the street or in the nearest homeless shelter (which is a nightmare hellhole) will quite literally kill me. I'm trying to get enough money to afford a place somewhere else until I can get a new job- there's a place nearby that does weekly rentals for around $140 a week, so I'm trying to get enough to stay there for at least a little while. Please, I hate asking people for things, but this is literally a matter of life and death.