Can a history of being on the bad end of child abuse cause an avoidant personality disorder?

Yes: If one was traumatized early in life then he or she can develop with a dread and paralyzing fear of most relationships (i.e. Avoidant personality disorder). I recommend psychotherapy to help with the intrusion of past, severe trauma on present relationships and life.

Avoidant: Personality disorder is a pervasive lifelong pattern of feelings of inadequacy, sensitivity to rejection, etc.. It’s highly doubtful that APD or other personality disorders, would be a result of childhood trauma. Trauma can make one susceptible to mood and anxiety disorders, most commonly. Regardless, seeing a therapist and a psychiatrist is the best recommendation given your history.