It makes a lot of sense to me @creative_writer , I've felt it before too - and often still do I can admit. Especially with how "not hoping" seems easier than trying and being disappointed if it doesn't help - and the longer this goes on, the harder and harder if gets I found for myself.
Did I read that there was a suitable psych you read about but just depends if they are the right interpersonal fit for you?
Have you had a chance to contact them / have a chat to get a "feel" for their personality?
I remember my first appointment with my current counsellor. I wasn't sure afterwards how I felt re: personality. She wasn't the same 'warmth' feeling that I got with some previous ones that I clicked well with, but I also wasn't getting the "nope, not for me" feeling that I had also gotten with some before either. So I stuck with it. And I think it just took a few sessions for her to understand how I think and my history (because it is atypical). I've seen her weekly for 5 months now, and I really like her. I can laugh and cry with her. I can be honest about any thought I have, even if I feel ashamed to think it or feel it.
I don't know if that is any encouragement for you or not; but maybe it will be. Either way, it is normal to be cautious about finding the right fit. And I reckon it would be totally OK to spend the first session not talking about yourself, and just building interpersonal rapport getting to know them and some common-ground between you. That can help also to establish a "safe conversation topic" to return to if things get too hard, a topic that is enjoyable and positive to talk about - like pets, or a hobby, etc.