First call your insurance company and find out the process for seeing a psychiatrist.
Armed with the correct information, you can go from there.
Sometimes doctor's offices insurance rules information is incorrect, so best to go straight to the source first. They can help you so you know just what you need to do next.

Ask your insurance company:
Do I need a referral to see a psychiatrist?
Can my GP-- Dr. X, refer me to the psychiatrist-- Dr. Y?
If not, how do I get approval to see Dr. Y?