Agoraphobia & Social Anxiety Support Group
Agoraphobia is an anxiety disorder, often precipitated by the fear of having a panic attack in a setting from which there is no easy means of escape. As a result, sufferers of agoraphobia may avoid public and/or unfamiliar places. In severe cases, the sufferer may become confined to their home, experiencing difficulty traveling from this "safe place."

I am assuming that this girl was/is your friend for a reason, and possibly prior to your difficulties with anxiety? If this is the case, and if she started attending the group sessions in an effort to support you, which seems likely, I would urge you to take care to preserve the friendship.
When you do as the previous comments suggest and tell her that you need a certain amount of space, it would be good to try to explain your reasons and make it as clear as possible that this need is in no way a reflection upon your friendship. The fact that she has attended some sessions may allow her a little insight into what you are dealing with and why that personal space is necessary for you to be able to function at your best.
Explain that even the truest and most supportive of friendships can begin to feel like a burden if you are not able to take time alone so your general and social anxieties can level out.
If she is really a friend and has truly been trying to understand the difficulties you face, she should be able to take your request for a bit of space as something that you need both for yourself and for your friendship. If she still wishes to learn about anxiety and such, perhaps there is a group or something for the friends and family. You could get her some literature to read over. Maybe you could invite her to join you for a group session once it a while, which would allow her to be involved/supportive, and you will have the freedom (for lack of a better word) to express yourself and discuss whatever you wish during the more regular sessions when she is not with you.
I hope you are able to find a happy medium and preserve your friendship. That being said, it is important that you do what is best for you. It is well and good to compromise and make allowances for those closest to us, but only so long as they are willing to do the same for you, and so long as you are not hurting yourself by doing so.
Best wishes
Hope I didn't ramble on too much :-)
Does this friend have some issues where she needs to be in the same group with you? Or is she there because you are? If she is there because you are there than I can see where you feel very fearful of sharing some things in the group. However, groups are meant to be confidential. Can you speak with the leader of the group to get her opinion of what to do in this situation?
It is obvious that you do not trust this person with the details of your circumstances. I would feel that way too. If possible I would move to a different group.