I think it is an odd place to cut. I have burnt myself there on oven racks, cooking, and other "natural" things.

Your T may or may not have similar symptoms to yours but that does not make her a hypocrite? All of us here are advising one another on how to work with our symptoms and problems and that's all a T is doing but from a more trained viewpoint. If she does SI, her "understanding" of your problems and feelings about it would be that much better, I'd think, than a T that does not. Too, it's the underlying problems we are supposed to be addressing in therapy, not the symptoms so much and no one has the same underlying problems?