A few things come to mind that may help: become a roommate, get a co-signor, and look for social services programs which may help you locate suitable housing.
Roommate: The benefit is someone else has qualified for the lease with their credit and income. You can be added to the lease as an occupant often without credit inquiry. If you go this route, you will want to see a copy of the lease so you know when it ends and can make other housing arrangements.
Co-signor: A co-signor can help a landlord feel at ease knowing someone else has faith in your ability to pay rent. Should you fail, they now have two people (you and your co-signor) from whom to seek damages.
Social Services: Take to Google and use every key word search you can think of, in hopes of finding an organization who offers help for: single moms, pregnant women, and the homeless. I understand you may not need their financial support - but what you are looking for and do need are their "contacts" for housing.