I generously suggested to a co-worker that she see my therapist. I expected she would be referred on, because she was battling alcoholism and that isn't something my T specializs in. When that didn't happen, and my co-worker let me know she had some appointments scheduled, I wasn't feeling very good, or nice, about it. I had a lot of issues about it, and decided to tell my T. Since they had only met twice at that point, my T told me that she would be glad to refer the person on. She asked me to think about it between sessions, then let her know what I thought. She said the final decision would be hers and she would let me know.
She decided to refer her to another T.

So, my co-worker got the help she needed (or would have, if she hadn't quit) and I got to learn that I wasn't comfortable with the jealousy around this, and around the possibility of seeing someone make great progress with "my" T, and worry and jealousy again about them hitting it off (while I struggled), and the fear of lack of confidentiality at work.

Your feelings about your friend seeing your T are good things to talk to your T about.