I get anxious and fearful before most of my sessions.
I think this might be something very interesting for you and T to explore. See if you can notice how this works with you, when it begins and what thoughts are there about it, how it progresses or stays in place, fears that might be there.
Your mentioning your old T sounds like there is a connection there to that experience and I think you are on to something there.
Most often when I take a look, it is my fear of losing T and it might even be combined with my fear of needing her too.