A.C.
Would it be helpful if you knew ahead of time whether you'd be called on to pray or read a passage? If it would, can you talk to the group leader and let them know that you have a diagnosed anxiety disorder, and that it would make it better for you to have a schedule (for you at least) of who is going to pray, etc.?
The other thought I had was to work on centering/relaxing, via yoga or tai chi (I have found I like tai chi better, personally), or meditation (choose a short mantra to repeat if you want to (G-d is good, etc.), then sit in a quiet place to sit cross legged on the floor, light a candle to help you focus if you want, and start with a short prayer or Bible passage; then, focus on relaxing your breathing and focus on the mantra and let all other thoughts pass through and out of your mind; it's hard work, but well worth the well being it provides), I've known people who suffer from clinical depression and anxiety to benefit from all of these practices.
I do think that you should not give up on this, or become reclusive--you have gifts worth sharing and deserve the friendship/support you can get from others!