Unfortunately, I think this becomes part of the process and certain parts of it, even require multiple opinions. However, you should consider this a good thing. Getting another's perspective on a fresh take from where you are now can be a good thing.
Trust me, I am very aware of the relationships we setup with our therapist. The pain I exposed to my first ever was completely overwhelming to that therapist. The rest of my therapists did not get to see that and to them its partially a loss. But each have helped me along the way.
Some I have liked (or I thought were more effective) than others.
If you decide later to go for any medical procedures like GCS, they will require you be evaluated by multiple people. Mine required at least one I provided (I provided 2, one a Psychologist - PHD), plus their own in house staff evaluations (bringing to a total of 3 for me). Since my Therapist was retiring at the time, I ended up continuing with the Psychologist, since she got to know me through the process for GCS. And I have been with her ever since. Although I generally think therapists are better (in my opinion), I continued with her because I didn't feel like starting over again with someone else at the time.
So, I get it. I share stuff with them that I will never share here. At some point, you have to be able to share the really personal things that we don't necessarily want to share with anyone else. That, in itself, sets up a very intimate relationship. And I attribute that to doing it right. If you have a fear or reluctance to share that with others...then I would say that you are doing therapy right! Just know that sometimes you have no choice but to change therapists.
I would love to have one of my therapists back. He was great, but he had to move to Florida (taking care of aging parents). And he considered face to face required; and I can see his point in that. I started with him reluctantly (I was looking for a woman at the time), but he truly ended up being my best so far. Once you go searching...you never know who you are going to find. Point is, approach the search with an open mind.
Best of luck!