ISO boy born between 1955-1961

Hello all, I recently discovered that my grandmother, Jo Ann McGee was sent to a home for unwed mothers here in Houston between 1955-1961 and gave birth to a boy via c-section. She would have been between 15 and 21 years of age. I have no information as to which home or agency it was, as everyone that would know has passed. The only living relative is her brother and he suffers from dementia. My grandfather, whom married my grandmother after the adoption, told myself and my mother about the baby. He didn't have any other valuable information though. If anyone could help, I'd greatly appreciate it, my mother would love to find her brother.