That depends. Only a psychiatrist can truly evaluate the medical aspects of your concerns, and only a medical doctor can prescribe medications. Sometimes starting with a psychiatrist is a good idea in order to make sure there are no medical problems underlying or masquerading as mental problems. Evaluating the medical aspect from the beginning may save you some time.
So, you don't have to see a psychiatrist unless you need to consider medication and/or medical problems. On the other hand, a well trained psychiatrist can see the whole picture and therefore make a more comprehensive treatment plan with you, including recommendations for specific kinds of psychotherapy. Only some psychiatrists offer psychotherapy, most psychiatrists only offer comprehensive evaluation and medication management.
If you only need or want psychotherapy, you can often get good therapy, at a lower cost, from a Psychologist, MFT (Marriage & Family Therapist), or LCSW (Licensed Clinical Social Worker), all of whom have specialized training in psychotherapy and the mental health field. The amount of specialized training in psychotherapy is less in descending order, however all therapists can augment their formal training and become specialized through additional training. Like in all fields, some individuals are more skilled than others.
M.D. stands for Medical Doctor. D.O. stands for Doctor of Osteopathy; D.O.s receive the same medical training as an M.D., with additional training for the osteopathy aspect.