ISO baby boy born between 1956-1961

Hello all, I am extremely new to this and searching for a baby boy my grandmother placed for adoption between 1955 and 1961 in Houston, Tx. All I know is that she was sent to a home for unwed mothers here in Houston and the baby was a boy. I don't know what home, but her name is Jo Ann McGee. She would have been between 15 and 21 years of age and had a c-section. My family is extremely vague on this subject and her only living brother, who was 14 at the time, won't say anything other than, "your grandmother did a bad thing and we don't speak about it." My mother is desperate to find her sibling.