I think I should go expose a friend's semi-secret social anxiety in front of our colleagues
What makes you think it is okay to expose your friend's secret?
She did not mind when I talked about her in front of our friends
Giving away a friend's confidence regarding her anxiety issue in front of work colleagues is improper. Keep the secrets your friend has entrusted you with or you will ruin your friendship.
It's not like I have a reason to not talk about it.
I think it's best you should keep these secrets since she entrusted you with them. She has social anxiety, so how do you think she felt when you told things in front of her? How about apologizing to her and let her speak on how her anxiety affects her?