There seems to be some confusion here.
1) Psychiatrists are MDs with a specialty in Brain/Mental health related disorders. Typically utilizing the Medical Model of diagnosis and prescribing to alleviate the disorder. They can be Psychotherapists or Psychoanalysts as well if they choose to specialize in those types of approaches.
2) Psychoanalysts have specific training in that particular approach and need not have a degree in medicine or even psychology for that matter.
This from the Toronto Psychoanalytic Society and Institute:
Admission criteria
Applicants normally possess either a medical degree or a doctorate in psychology, social work, the humanities, or the social sciences, or a master’s degree in social work. A background of clinical experience in psychotherapy is strongly recommended for all applicants. These criteria ensure that candidates will be studying with classmates who are experienced and sophisticated
clinicians and scholars.
Suitable applicants will be interviewed by three separate members of the Institute Admissions Committee. The reports of these interviews will then be considered along with the applicant’s
curriculum vitae and letters of reference.
3) Psychologists cannot prescribe meds as they are not MDs. They utilize a variety of approaches depending on the personal preference of the individual.
4) Counsellors do not necessarily have a PhD and could only have Community College courses to be licensed to practise in Ontario.
Here is a superficial overview of the types of psychotherapies.
http://en.wikipedia.org/wiki/Psychotherapy
http://www.strisik.com/therapy/approaches.htm
Ask your current therapist to refer you to someone else. Explain that you don't feel that you are making progress and do not anticipate the situation getting any better. If they are ethical and competent they will be happy to refer you to someone else who may fit your needs. If not contact the Ontario Psychological Assoc. or your family doctor.