A good therapist will meet you where you are. You control therapy. You control what issues you want to present and the speed you want to process them.

I was a little like you describe - I first went to therapy with certain history that I wanted to give her and basically cried through the whole thing. But there were additional issues that cause(d) me deep regret, grief and shame that I held onto a long time before I trusted she might be able to handle knowing about them.