Well, it would be hard to get around your PCP without a referral on that one due to insurance companies these days . I have seen both and actually right now am seeing both a psychiatrist and psychologist (who is basically a counselor with an advanced degree minus the MD).
The only problem with not being assesed by a psychiatrist is 1). your not going to know what your firm diagnosis is which is necessary to know when a doctor of any kind is prescribing medications. 2). you may run into a break down of communication between the psychologist and your primary doc since all of your psychiatric records are keep confidential even from your PCP. Then 3). psychologists can make recommendations on what they see during your sessions and some may even recommend to you a change in medication but since they are not MD's they can not by law recommend a specific medication or what might work better for you during that time. So in my opinion that is where psychiatrists very much out weigh the psychologist.
Plus keep in mind that you dont have to see just one or the other, you can see both. If you went to see a psychologist who is in a private practice you could always ask to see one of their psychiatrists for medication maintance. Of course that isnt all they do for you but the psychologist could push your PCP for a referral once your in the door. You have many options open to you here.
Please do keep us posted...Take care dear