Maybe you jack yourself up on caffiene before group.
Imagine what the group would say if you came in one session and dominated the whole thing, not letting anyone else get word in edgewise.
But seriously, I'm glad that you explored it with your T during individual. It makes perfect sense that you like to think about what you are going to say beforehand.... and sitting in a group while everyone is waiting for you to talk isn't really an ideal situation.
Maybe you can commit yourself to saying just one thing about yourself next week. Just one. I know that group discussions can end up going wherever the group takes it and that you can't always plan beforehand what you want to say... but perhaps, knowing the dynamics of the group, you can think up a couple of things you might want to say-- something will fit in-- then pick one. And that's it. Then you can decide how you feel when you say it, and whether or not you feel like elaborating. If you do well, buy yourself a new outfit for indivdual on Tuesday. And if you you don't do well, then still buy an outfit. Just don't buy shoes to go with it.