Everyone gave you excellent answers, and they are all true. Your T will NOT be horrified at whatever you tell her, and she will not think less of you. She will be proud of you for being able to share some of your pain with her. But you can do this at your own pace, like others said. No need to say anything you're not ready to.

I know my stuff is not so awful, but even so, I am terribly embarrassed and disgusted with myself when I tell her my T what I tell her. I want to hide from her. But she makes everything okay with her reassurance and praise for my feeling safe enough to be so honest with her. She makes it okay to tell.

You can risk a tiny bit and see how you feel. If it's too hard, stop. Ts don't expect everything to come spilling out at once, but if it does, that's okay too. That's why therapy is so great; anything is all right--in how you tell your story.