I think you should speak with her about all of this directly and frankly.

Did you give her permission to speak with your GP about you? I think discussing this and your feelings about this is extremely important. Because the privacy and confidentiality of your session is paramount.

I don't know you, or what has led you to therapy. But the therapy experience can be a laboratory to explore your feelings and expectations about others, in case your perceptions are related not so much to your therapist's behavior but rather to your own assumptions based on past experiences.

Your therapist may not be the right fit for you. But maybe the two of you could discuss all this and grow closer. Tell your therapist you are not sure you can trust her. Tell her why. This is all fodder for therapy. If she reacts defensively or can't discuss this and her own potential contributions, that would be red flag to me. But maybe if you just take a risk and be honest about your feelings, she will either develop new ways of interacting with you or share more about her perspective so you can see where she is coming from.