She is a Chartered Clinical Psychologist therefore she has a doctorate and so is a Doctor, but not in medicine, also psychology is a science. She wouldn't actually prescribe anti depressants as that is something left to psychiatrists (who are medical doctors who have undertaken further training in psychology). Clinical Psychologist would prescribe, what is termed these days, as talking therapies e.g. CBT and would not psychoanalysis you as that is something a psychoanalyst (who doesn't require a doctorate) would do.
That all said, albeit in a confusing way, I have no respect for her any more with the cobblers she comes out with. I'm so glad that I didn't do my PhD with her, as I would hate to be associated with any of her non-scientific nonsense!