A Psychiatrist is only seen once every few months for about 10 minutes for a med check and to give out prescriptions. They do not do counseling. If you don't need meds then you have zero need to consider a Psychiatrist.
Depending on their degree a counselor, therapist, and Psychologist are basically the same thing. Sometimes a MSW or even a LPC could be the right choice for you.
An MSW is a Masters degree in Social Work. It is a world wide recognized degree that is usually accepted by any insurance.
An LPC is a person who has a Master's degree in some social science such as psychology that has tested and has received their certification that allows them to hold a license to perform and bill 3rd party insurance for services provided.
A Psychologist is a person who has a Doctorate in Psychology and is licensed as a Clinical Psychologist to treat patients and bill 3rd party insurance for payment.
A therapist often tends to treat one ailment or another, such as panic attacks, OCPD, or depression. I think most have one primary focus they really do well in and they do a good job in that area. They can bill 3rd party insurance too, although they can be just a Bachelors degree person they are usually in a clinic that has a primary Psychologist that is the "Supervisor" so they can bill under that persons name. I always hear the term used in drug and alcohol treatment. They often have several college students and one Psychologist on staff and do staffing's on the patients so the Psychologists is supervising this person's care.
There are many many people out there who proclaim to be licensed and are able to help. Please just call your insurance provider and get a list of who they will pay for services. That way if you do find someone that you click with you'll know if they are even an option.