What is the price range for Psychiatrists?

Because I’m going to try and make an appointment with one maybe and I know my parents will want to know why since I have to tell them the info for insurance.

They won’t let me call insurance and they won’t trust the doctors when they say they are covered so I have to give my parents the information and hope they call?

But they won’t understand why I need a psychiatrist so maybe I have to just make an appointment and pay out of pocket.

I am lost I don’t know