My girlfriend had a huge secret and I outted it accidentally.
Accidentally? How did you do that?
I said a word to my friends about a concealed secret that she kept. I felt so sorry afterwards.
Your girlfriend might be very angry at you for revealing her secret, and she has a right to be. However, once she understands that you didn't mean to cause any harm, and you simply let the wrong word slip out, she'll likely forgive you.
Whatever.
You should just tell your girlfriend and let her get disappointed at you, because sometimes that's all that you can do to make things better. Don't be too upset, because fights like this are normal and healthy in a good and strong relationship.