Hairy: If you don't work, then you probably won't get a fine for no health insurance. There is no fine just for not having insurance. The fine is for having enough income to be required to have insurance and not having it. If you don't have any income, then there is no fine.
If you don't work, do you have other income? If your income is too low to be required to file a return there is no penalty. You can file for Medicaid on your state's exchange website, or if they don't have one, on the federal one at healthcare.gov.
If you live with Mom, her income has to be included on the application. If you lie and dont put it down, you are guilty of federal fraud. Also, you have to live in a state that expanded Medicaid under Obamacare for those who are not disabled or on SSI.
You have to qualify for welfare before you can get it. The qualification will depend partially on your state of residence and also on household income.