I guess I just need to come out and be honest with her, right?
Yeah!
You're on day three. It's probably going to get a little harder before easier. Especially between now and then. Which is why (I know I sound like I must be hounding you by now) You might want to try a meeting. Within my first 30-days of meetings I had a nice small support circle. I had to go out to a party right around then. I was able to bring one of my new "friends" with me to help me not drink.
I had to come out of the closet to everyone. I was a seasoned closet drunk. When I told my sister, she was nothing but supportive. I did eventually have to tell some of my dirty secrets because they didn't believe me!
Telling your sister will make it real. Have you actually said it outloud yet? "I'm an alcoholic"?