That is the million dollar question that even an American born citizen has difficulites to figure out. Unlike Eupoean coountries with less population and size, the story gets very complicated here in the US. That is one of the reason why the health care and anti immigration sentiments collide. Imagine all the free health care the illegial enjoy, how much it drains the resources of the government esp in cities with huge Latin American population. We are talking millions of people and billions of dollars given to people who have never paid a dime in tax money. How fair is it to people who abide with the law and pay their taxes and their insurance on time?
Your best luck will to find "under the table" type of small clinic operated by immigrant doctors, or find a local low income hep center and find a way through them.
Good luck.