Bad At Secrets

I am so bad at keeping secrets--sometimes I don't even realize that I am sharing things that I am not supposed to be sharing!!

But the most recent case has been so sad for me.  Since about September this year, I was becoming really good friends with this girl in my class.  We shared similar interests but but didn't have an ordinary relationship.  Neither of us like to share our emotions so our friendship and care for each other was kind of something that was understood and never spoken. 

A few days ago, I told a secret that she didn't want me to share with anyone.  Except, I didn't know it was a secret until AFTER i told someone else.  This obviously isn't justifiable to my friend whom I hurt.

She says she doesn't trust me anymore--I don't know what I can say to get her to trust me again.  I don't want to be too emotional or sad because niether of us are like that.

Am I a bad friend for breaking her trust, or was this an unfortunate coincidence that I told her secret BEFORE it was a secret??

THANKS FOR YOUR HELP!! <3