“Child” means any person under 18 years of age. For purposes of admission to and residence in child care institutions, group homes, and maternity centers, the term also means any person under 21 years of age who is referred by a parent or guardian, including an agency having legal responsibility for the person pursuant to the Juvenile Court Act or the Juvenile Court Act of 1987. Termination of care for such persons under 21 years of age shall occur no later than 90 days following completion of a public school secondary education program or the individual‘s eligibility for such a program.