Good luck--I hope you can find someplace quickly. This is another way that calling the shelter might help. They are often able to help find housing for victims who have to leave their homes due to abuse, even if you don't ever stay at the shelter. The Advocacy Unit at the prosecutor's office where I used to work would collect furniture and other necessities to help set up new homes for women who had to leave with their kids. I donated a bunch of things when I cleaned out some old furniture etc. that I had.
Hopefully you can also get child support (and maybe even temporary spousal support), which will help with expenses. Do you have a job or other income?