It doesn't sound like she has anything to offer you, so why go? Working things through is one thing, but working things through with someone who has nothing to offer you is quite another. I personally would only work out conflict with a competent therapist who I liked, respected, and felt confidence in.

That's great you have a great relationship with your GP, and I bet she could refer you to someone. If she doesn't know of anyone in particular, perhaps she can ask her colleagues. I know what it's like finding a decent therapist. Finding a good one is no easy task!