MRCS LRCP Lond 1894.
Barrow was educated at Owens College. In 1894 he was appointed house surgeon at St Mary's Hospital Manchester. Barrow was AMO at Manchester Consumption Hospital and County Asylum Whittingham, and medical officer for the Hospital for Sick Children, Manchester. He was later appointed honorary anaesthetist to Manchester Northern Hospital for Women and Children, Ancoats Hospital and Jewish Hospital Manchester. Barrow was also anaesthetist to the Ear and Royal Eye Hospitals in Manchester and medical officer to the Police Court. He died on 30 May 1945.