Hi zinco, really sorry you're feeling this way but it is really good that you're recognizing you need support, and are wanting to/trying to reach for that
But the groups............"All" it needs to begin with is a phone call, yes? And in that phone call (to the group organizers?) you can explain your anxieties and find a place to start e.g. they could explain the groups setup, you could arrange to see them on their own first, you could just go to the end of a meeting (less pressure), you could let them know that you might not want to talk on the first meeting so to avoid coming to you, if there are different groups then maybe they could arrange for you to go to a smaller one...........I'd think they'd want to help you in attending in a way that feels comfortable/OKish to you.
And the motivation to go.............**** of a lot of self talk maybe?? Don't let up on yourself, whatever?? It is clear you want this, just that first/those first step/s...........And maybe there's someone you can ask to try to help you give yourself that push?? As well as us!!
But feeling like a burden to your family/friends..........remember that depression can all too often make you feel that regardless of how they may actually be feeling about supporting/being there for you. Please try not to cut them out too much, it might just be that they really want to be there for you.

Alison