I tried very hard to locate information about this topic for you, but there is not much to be had on Higgins and the Oedipal complex. I did find one article, from 1958, titled "Shaw's Childhood and Pygmalion," in which the author, Philip Weissman, argues that Shaw's early life is reflected in the character of Henry Higgins. The full article, however, is not available without subscription.
You may be able to create an argument about Shaw filtering his own problems through Higgins by examining the author's early life. Another source reports that, "Lucinda Elisabeth (Gurly) Shaw, his mother, was the daughter of an impoverished landowner. She was 16-years younger than her husband. George Carr was a drunkard - his example prompted his son to become a teetotaller. When he died in 1885, his children and wife did not attend his funeral. Young Shaw and his two sisters were brought up mostly by servants. Shaw's mother eventually left the family home to teach music, singing, in London. When she died in 1913, Shaw confessed to Mrs. Patrick Campbell: "I must write to you about it, because there is no one else who didn't hate her mother, and even who doesn't hate her children."