Karie,
Have you checked with Planned Parenthood? I know that they do provide some family medical care.
Have you also checked with local charities, like the Salvation Army? Sometimes they can assist with medical costs, depending on your situation.
What about your local church/synagogue/temple? There are sometimes members of these religious communities that work in the medical field and donate some of their time to their spiritual community.
By all means, if you KNOW you qualify for state aid, keep pestering case workers. Your situation is EXACTLY what state aid should be for.
I was only able to manage a small bit of research for programs in IL--work is very busy for me today--but the link below might be able to give you some more options on places to contact.
Health & Wellness - Woman