Apply for Medicaid if you are the parent or guardian of a child who is 18 years old or younger and your family's income is limited, or if your child is sick enough to need nursing home care, but could stay home with good quality care at home. If you are a teenager living on your own, the state may allow you to apply for Medicaid on your own behalf or any adult may apply for you. Many states also cover children up to age 21.