No one, not even your parents, have any obligation to pay for your college (unless your parents are divorced and one of them promised to do so in the divorce papers). Once you reach the age of majority in your State (it's 18 in mine), you can live where you want and no one has the support obligation. If still attending high school makes a difference in your State, you can call and ask social services.
We do not have an attorney-client relationship. I am not your lawyer. The statements I have made do not constitute legal advice. Any statements I have made are based upon the very limited facts you have presented, and under the premise that you will consult with a local attorney. This is not an attempt to solicit business. This disclaimer is in addition to any disclaimers that this website has made. I am only licensed in California.
As an 18 year old you are an adult and can do what you want. You can continue to attend the same high school if you continue to reside in the same school district. No, a family that agrees that you come live with them bears no legal or financial responsibility for you.
Under the circumstances (i.e. that you feel compelled to leave your parents) I suggest you reach out to social services (or maybe just start with your guidance counselor) to see what kind of services and assistance you may qualify for.
I would need more information - specifically - are your parents divorced and is there an agreement in place regarding custody, child support, emancipation, etc? If there is no agreement and your parents are still married, they do not have an affirmative obligation to provide aide for college. It would be optional for them whether you were living in the house or not.
This answer does not constitute the establishment of an attorney/client relationship nor is there any guarantee that this advice will be completely effective in a court of law. A consultation, including review of court orders and other documents is necessary in order for me to give you proper advice and guidance.