Most, if not every insurance company, will cover psychiatrist (MD) and psychologist (Master or Ph.D) service if you are talking about US insurance policy, since this is a kind of big issues in this country. You will need to call your insurance company and get pre-approval on the phone.
Between psychiatrist and psychologist, I recommend you to see psychiatrist first, who has the prescription right. They will refer you to psychologist if psychotherapy is needed.