Hey, I'm sorry to hear you're in that situation. I've had the rough sleeper/homeless shelter experience. I'm male and live in an EU country so my experience will most likely differ from yours but here's what happened to me.
TL;DR: It wasn't as bad as I thought, you just keep your head down, get a job, apply for better homeless accommodation if you can and make sure you're safe.
I left my home due to the people I was living with selling their house. I had no savings since I spent it all on booze or food. I was scared shitless and having arguments with my landlady until I eventually left before she could kick me out.
I spent around two or three weeks living outside the mall I worked at. I would stay awake all night from 11pm-12am when my work closed to 5-6am when the mall opened up for cleaners. I would sleep in the staff room. That stopped when my manager forced me to stop sleeping there. I hid my clothes in bushes near the mall. Eventually I got a small storage container and kept my stuff there until I could secure a hostel room.
Eventually I got in contact with a homeless charity that helped me get a room in a homeless hostel. It was a three man room with my own bed and place to put my stuff. My roommates were loud but were harmless, one was a really bad alcoholic who barely spoke English and the other spoke no English but was straight edge. I moved from room to room until I found a two man room with a very understanding and friendly roommate who looked out for me.
After a year and a half of applying my application for a one room homeless accommodation was accepted and that's where I'm currently living. Despite my CBT plans I'm very grateful for where I'm living, especially with my country's ongoing housing crisis. Things do get better, even when you've hit rock bottom you just got to fight for yourself. Easier said than done but it's worth it.