Unless NY is really different from the rest of the country, psychologists can't write prescriptions. They are currently lobbying for that power, but psychologists are deeply divided on whether or not to be involved in that. I know my psychologist opposes having that power. As to whether to see a psychologist or psychiatrist, the problem is that psychiatrists on health insurance plans don't do therapy; they hardly know meds. It's hard to find a good one, and you'll probably find when you start calling the names on the list that half or more of them don't even work with the insurance company, they're just listed because they have to take insurance at hospitals. So first find out if there's even a good one who's taking new patients. My own opinion is, if you want therapy, see a psychologist, just because they're cheaper and most have actually studied psychology much longer than psychiatrists, who spend most of their study learning meds and go to school for a much shorter period of time than psychologists. Consider: most psychologist have an undergraduate degree in psychology, that's four years, then a graduate degree in psychology, at least four years. Whereas psychiatrists have a pre-med undergraduate degree most likely, a medical degree, then one year of psychology, one year of psychopharmacology and neurology, and then one year of residency in a hospital. So my preference would be to see the psychologist for therapy, saving money but not losing any expertise, and seeing the psychiatrist a few times a year for medication consults if the therapy doesn't work for you.
I would suggest contacting the American Board of Psychiatrists and asking for several referrals. Psychologist are also allowed to write perscriptions, so ask for the names of several of those as well. One of the most important aspects of therapy is that you like your therapist. If you don't, you won't get anywhere. That is why I recommend you get several and make appointments to check them out. This is a very normal and accepted procedure and you should not feel guilty in any way if you're not comfortable with any particular one of them. They will understand. You will not hurt their feelings! And even if you do, that is why psychiatrists go to psychiatrists! (LOL Really!)
If your insurance only covers therapist, they can still recommend medications for you, the actual script just has to be written by your doctor, but the three of you should be working together anyway.
If you don't get any help from my suggestion, please post again and hopefully someone else will have a better idea than mine. We'll find you some help, you can count on that!
Peace
Greenlydia