Insurance companies usually have lists of the providers they cover. Maybe you can get that list? Call them and they should be able to email the list or it may be available on line already.
Then the best thing is to get referrals. Ask you primary care doc/ ARNP if they can recommend anyone from the list. Your first psych's office may be able to help too. They understand this changing insurance thing. A school conselor may be able to help.
Another idea is to join a Chronic Fatigue Syndrome or Fibro support group. Or any group really that deals with chronic illness. Ask around and see if there are some psych's they have had good experiences with.
Hope you are able to find one that "clicks". They are a valuable resource in dealing with anxiety, depression and chronic illness.
It is important to find someone that will listen to your concerns and discuss them with you. You should feel comfortable enough that you can really open up about how you feel and tell them what is going on. This is one of those things where the more you open up, the more they can help you.
I'll have to find a new psych too cause I won't be able to afford the out-of-pocket anymore. I haven't started looking yet. It makes me cause I really like the one I have now and she has helped a lot.