This T seems very unprofessional. I have been seeing mine for 6 months and he's never once looked at his phone (I've never even seen it in his office, actually) or ever made me feel like I don't have his 100% attention. He does leave silences quite often, but it's to give me room to think or perhaps to give me space to say something that's going to be difficult. I never have felt like we had run out of things to talk about.

There is absolutely no excuse for her behavior. If she was texting on a date you'd probably feel uncomfortable (even angry) and your sessions are no different. You have a right to her full attention.