I don't think going to the shelter is going to help right now. You'll have even less privacy and space. I feel your pain. Hang in there.

Now, you need to confront your mom. Ask her for specifics (ask your mom first to see what she was told.) Ask about the place this woman is moving to, how many days specifically, and say that after that she has to go. Then, ask the lady (without saying you talked to your mom,) if she has any leads on a place. See if she gives you the same answers. Then you'll know if she lied to your mom.