Some things you can do: Contact the local child support enforcement agency, because if there is an existing order for support, the state has tools at its disposal to find your child's father that you may not have. See whether your ability to get private or job-related insurance has improved through the Affordable Care Act ("Obamacare"), which limits insurers' power to shut out children based on preexisting conditions. Talk to your local legal aid program on how to get information on any publicly funded benefit programs that may exist to cover your child's medical care. Once you have locked in insurance to cover future costs, talk to a bankruptcy lawyer about discharging the old medical debt.
Disclaimer: This site exists to provide information only. It is not legal advice. Answering your question does not create an attorney-client relationship. I am a Massachusetts lawyer. Any information provided on this site does not, except as explicitly stated, imply familiarity with laws or procedures peculiar to your state which may differ from those where I practice.