Sherman was born in Evanston, Illinois, to Walter Allen Stults and the former Monica Graham. She graduated from Evanston Township High School and attended the Institute de Mme Collnot in Paris, France. In 1934, she obtained her bachelor of arts degree from Northwestern University. The following year, she received a Master of Arts degree from the University of Chicago. From 1935 to 1936, Sherman was an instructor at the University of Illinois French Institute in Paris.
In 1943, she obtained a medical degree from the University of Chicago. She interned at Bob Roberts Hospital at the University of Chicago. In 1947, she was appointed assistant professor of orthopedic surgery at Billings Hospital, also affiliated with the university. In 1952, she relocated to New Orleans to become director of the bone pathology laboratory at The Ochsner Clinic Medical Foundation, a creation of surgeon Alton Ochsner. The next year she began her terminal position as associate professor at Tulane Medical School. A cancer researcher, she was also the senior visiting surgeon in orthopedics at Charity Hospital in New Orleans.
In the hours before dawn on July 21, 1964, Dr. Sherman was found dead in her apartment on St. Charles Avenue in New Orleans. The police report classified the death as a murder. The autopsy report said her right arm and rib cage had been burned away, yet the hair on her head remained unburned. A small fire had been set in her apartment which burned the mattress and some underwear, but no witness reported seeing a flame. The body had been stabbed in the heart, liver, arm, leg, and stomach. The wound to the heart was determined to be the precise cause of death. This wound hemorrhaged, but the wound to the liver did not, indicating that she was alive at the time of the heart wound, but already dead by the time the wound to the liver was inflicted. Investigators determined that the massive burns inflicted upon her could not have occurred in her apartment. The details of her missing arm were not released to the public.