My son's father pays for our son's health insurance through his employer. Can I get gov insurance for myself?

We are not married and I need health insurance. Marriage is not an option right now. I am looking to apply for a government insurance but I am not sure how it works or how my son being covered by his father would affect me. Any one with this situation? Any suggestions?
--------------------
You could try for Medicaid or get a job that has ins.
Source