You are getting great advice here..
Every action gets a reaction...I don't know her, I don't know how she will react or feel. She could feel like she was made a complete fool of, or wonder "Who are you??"
You did steal from her, you stole her right to the truth.
I would keep that in mind now you have told her you are an alcoholic.
Why do you want to tell her, for you, your conscience or for her and her right to the truth.
I also wish you the best and hope it goes well.