it depends on what insurance you have. if you bring your insurance card to the doctor's office, the doctor's staff could phone the insurance company when they set up your appointment and see if they accept the insurance company's terms and what your co-pay might be. usually there is a deductible before payments kick in so i guess you'll be hitting up your parents for something but that's a helluva lot better than letting depression kill you kid.
if you just need a therapist, the doctor will tell you that and maybe give you a reference to a psychologist. generally a therapist can't write you an Rx if you need one so the psychiatrists work with psychologists.
also if you're scared to do it, at least talk to your family doctor and let him screen you for depression. he can call a shrink for you. the shrink is an expert though and your family doctor isn't. there are also free screening days at some hospitals in new york. if you live in manhattan call payne-whitney mental hospital and ask for general info.
good luck kiddo,
pi