Generally speaking, permanent resident aliens are eligible for MEDICARE (which is age based) coverage after 5 years of lawful residency in the United States.
MEDICAID (which is need based) coverage depends to some extent upon the laws of the particular state in which you are residing.
Generally speaking, Medicaid coverage also requires 5 years of lawful residency, but some emergency benefits (such as food and catastrophic healthcare) may be available sooner.
You should consult with your local Department of Social Services. Even if you have not yet had residency long enough for full coverage, you may qualify for some partial benefits that could help you out.