It does seem a strange and awkward situation. It sounds a little bit like when I was seeing a counsellor in university, she was quite open about herself and we talked about some of my issues but it always felt very surface level, is that how it feels with her? Do you feel like you are missing a deeper connection with her?
It may be that she isn’t trained so not allowed to talk about your deeper issues and how they could be worked through. I volunteered with a mental health phone line a while ago and we were trained to listen and mirror what people told us, but we weren’t allowed to give advice or discuss diagnoses and things reserved for professionals. It was quite frustrating when the people calling clearly needed more help than we could provide.