I'm sorry you're having problems with your insurance. Sounds like you have an HMO which is not the best insurance option to have when trying to get access to mental health providers and services. That said, is your GP part of the HMO network or are you paying out of pocket to see the GP? If GP is not covered by your HMO, then make an appointment with one that is and have your GP call the new doctor to relay the urgency of your situation.

Another reason the Psych Dept might have rejected the refferral is that some psych Depts at teaching hospitals only accept paitents who have been admitted as inpatient which most likely required the referral of a doc practicing at that hospital, either in emergency or critical care. I'm not saying you should take that route, but that would be a fast track to being "approved" by the psych department.

Alternatively, you could look at your community mental health options; is there a reduced cost clinic in your area? Or one dedicated solely to mental health? They ususally have a psychiatrist or two there and will take walk ins but you might have to wait a while. Appointments usually are booked for three months or more but they have a lot of cancellations or no shows, hence why walking in might be faster. Good luck!