Reinstatement of Enrollment for Medicaid Eligibility of Disadvantaged Youth (REMEDY) Act - Amends titles XIX (Medicaid) and XXI (State Children's Health Insurance) (SCHIP) of the Social Security Act to require a state plan to provide for the reinstatement to enrollment for medical assistance and child health assistance upon release from a public institution of an individual youth who was enrolled for such assistance immediately before becoming an inmate of such institution.