How do I fix what I've done?

I used to be this special little girl that my mom would always brag about and she would say to her friends how she never has problems with me being a bad kid. This put me kind of on a pedestal that I had that I had to keep up with up. Well, one night I went to my friends house and I was really in the mood to have fun. So, I went in to her kitchen and I took some of her dad's (I'm not sure what it was, but let's just say it was:) Vodka. I'm not sure how this came to be, but there was something urgent and I had to come home...drunk. So, mother's intuition kicked in and she knew right away and there way no way to hide it. She punished me and that was that. But, another thing happened that pushed me further down a hole. She was moving one day, while I was at school and she found a not to my friend saying that I'm going to quit smoking (cigarettes). She thought i was smoking Marijuana, but I guess it doesn't make it any better that it wasn't. Smoking is smoking. So, now she doesn't trust me. I have to wear my hair in a ponytail, no make up, and I can't go to my friends houses. Understandable, but I can't stand knowing that she doesn't trust me. How can I prove to her that I've changed my was and stopped all of the foolishness? I love her dearly and I hate to think that she looks at me and thinks about what I did. I want to make her happy. help?