I think you're saying a lot here.
Yes, like you I often think T is tired of me and my 'stuff'. I tell her when I'm feeling that way. It segues into my thinking she wants to be rid of me, wishes I'd never shown up, that I'm incredibly boring,, etc.
It does feel different to be missing T when we are away from T versus missing T and knowing T is not in the office. Sometimes weekends and long weekends are hard for me for that reason. Maybe you could journal or spend some quiet time thinking about T to make a connection in between sessions.
I also think you're saying you feel that T's MS diagnosis affects you too. It sounds like you worry about being "too much" for her. But it's up to your T to monitor her stress. It's important that you don't feel you need to do that or a need to be cautious. I hope you'll talk to your T about how you're feeling, even if you and she have already talked about it.
Feeling lonely for T is really so hard