Just so you know, you may have transitional housing available to you as someone looking to get out of domestic violence, housing that may not cost you at all.
I'd suggest following up with these resources now: no need to wait until you can afford rent. They may be able to help you find affordable, or even free, temporary housing to help get you out of abuse and over the housing-issues hump.
When talking to the YWCA, specifically, know they can likely help you with both these sets of needs: both getting out of the domestic violence you have been living in AND help getting counseling and/or support groups to heal from the sexual abuses/assaults. Just be sure to ask about all those needs so they know.
Never doubt that a small group of thoughtful, committed citizens can change the world. Indeed, it is the only thing that ever has. - Margaret Mead