Maybe you could voice some of your reservations with them in order to see if they can adapt & adjust? Then maybe somewhere along the way, they can "meet you in the middle..." It's maybe going to be the most feeling like an interrogation during that initial assessment period. Kind of like being thoroughly vetted by your lawyer, so that there are minimal surprises along the way. I guess they always like to know things in advance. Sometimes, at the expense of our own sanity & well-being (I'm over-stating, or emphasising, of course; just to make a point) / which is only that what you've just described as being your first experience with them, is pretty much what a lot of others would have subscribed to, too. . .
I'd agree that I think it is worth a shot, and to give it your best effort, for the risk is probably worth the reward - especially if it helps. You can decide and determine as you go how satisfied you are with the process. But generally speaking, and this is from primarily my personal experience, therapy can be a bit like mental gymnastics. And at times, verbal sparring (sessions). I'd always thought of it as, or equated it to, working out only for or with 'the mind!'
That said, with some heavy lifting, and hopefully not too much damage incurred, it can help you to overcome (over-time, you've got to have patience even in the best scenarios) some of your obstacles. Or be better prepared to handle & deal with them. At some point, if you feel there is a bad mixture with your therapist, you might be able to request a different one, just to see if someone is a better fit (for you).
I remember one of the smartest people I've ever known, telling me that when she was embarking on her pH. d at University, that it took her something like Ten Therapists in order for her to find one that she felt was acceptable. She'd told me that it was a place where she could go and express her thoughts, and herself "freely," without the fear of judgement being passed.
So anyways, I wish you the best of luck no matter what you decide!