Cincinnatti Hospitals 1904

Does anyone know how to find out which hospitals were open in Cincinnati in Jan 1904? I am trying to locate a birth record for my great-grandmother born 24 Jan 1904 in Cincinnati to a 16 y/o unwed mother. She may have been given up for adoption, but was later reunited with her mother. I have been unable to locate a birth record for her in any of the usual locations. Thanks so much!