From my experience with therapy, there is a kind of "uptake" time which it not unlike that with medications. You and the therapist need time to get to know each other & and to settle in around the issues you'll be focusing on. For me it's a kind of dance, and we get closer as time goes on.
The fact that you're comfortable enough to talk with this therapist is terrific. It makes me think that you've found someone you're going to be able to work with. Try not to worry about the expense for another six weeks or so--go with the flow. If, by then, you're still doubting whether therapy's for you, revisit the issue with your pdoc.
From what you've said, though, I think you just need to get past the break-in period. I always feel uncomfortable in that initial period--although after decades of this, my break-in time is pretty short.
Roadie