I've been homeless 5 times. It's terribly anxiety provoking and disheartening. When I was young back in 69, there weren't any homeless shelters.
My first real job was at a resort hotel in Cape Cod. The hotel provided lodging for workers for $1 a day, which was a fraction of my earnings. They also fed us twice a day, anything on the menu. I don't know if there are any such places left, but it's worth looking for them. Summer camps provide food and lodging as well as a salary, and it's fun to work with kids. It's late, but often summer camps have a second 'session' in July or August that lasts until Sept. The Forest Service also provides some lodging for certain kinds of employees.
If your mom is refusing to work and won't get sober, she is dragging you down. Try to find a way to separate from her so you can get off the streets at least by yourself.
Some states provide much better benefits for homeless people than others do. Check online at your local library for this, and on YouTube.
Some people live in state or national forests during the warm months. If you can't afford a $100 tent from Wal Mart, you can make your own shelter out of very inexpensive materials. There are dozens of tutorials on YouTube about how to do this. I used to sleep in public parks in out of the way depressions, which were invisible at night.
The important thing is to get a job, as school probably isn't as urgent a need right now. Maybe all you can get is a dishwashing job. I've had dishwashing jobs. They're not exciting jobs, but they're low stress, and once the work is done, it's done - you don't go home worrying about things you haven't done yet. Good luck!