If you want to keep seeing her, make it work. Her being concerned that you may need more support or expertise is a caring, helpful comment (especially if you keep telling her she's not enough and is going to leave you). It's not so much whether another person can help or not as whether we are willing to use what help is offered. If you want to work with her, make a decision to quit pushing her away and practice following through on your decisions. I decided not to do "fetal position" either literally or emotionally so I just kept talking, kept trying, kept going through tears, terror, whatever. I was in therapy because what I had been doing wasn't working (not because my therapist could do X, Y, or Z "about" me and my thoughts and behavior).

Decide to quit saying "no"? Doesn't matter how many degrees or what training a therapist has if you won't let them use it.