Some psychiatrists probably don't accept insurance because it means they will get less than they charge for payment from insurers, and the money is important, just as it should be for you. You selected one of the more expensive ones as your specialist.

I agree that it might be good just to meet with the other psychiatrist once, then
decide. Going into your savings isn't good; I agree with you on that one, too.
You need to be in a situation that permits you to have care without draining all
your resources.

Either way, money is part of your family's security, but your health is priceless.

You'll make the right decision, I feel.