Maybe this decision partly rests on how much of a disability your anxiety is in your day to day life?
I'm not questioning that anxiety is horrible, I suffer from it myself. But if you're able to somehow push through and work on your career etc., then maybe one day you would get to a place where you had a different insurance that would cover this treatment, or you lived in a different area or state where more was available, or you had more money.

I just think that this is about balancing up the stress your anxiety puts on your life vs the effect of putting yourself into financial stress. Personally I would err on the side of avoiding the loan - unless the anxiety is so disabling that day to day living is impossible - but on the other hand shouldn't the insurance cover it in that case...?

Sorry if this is not helpful!! I'm sure you'll do what you think is best and that's all any of us can do, isn't it?