I think my mom is an alcoholic. What do I do now?

My mother is completely “normal” in the day time, but it has become clear to me that anytime after 10pm she becomes a different person. I live upstairs, and downstairs I hear her tripping, falling, and knocking things over. She reeks of alcohol in the mornings, and doesn’t have a clue. I just woke up an hour ago to the sound of her knocking over a shelf and had to carry her to her room. My brother is 17, lives at home, and is completely oblivious to her drinking (he thinks she sleep walks). I’m so heart-broken and so afraid that WHEN he finds out, he’ll lose respect for her (just like I have). I feel like I need to continue living at home so I can keep her from hurting herself and prevent my brother from taking up my ‘job’.
We live a very fortunate life, and I can’t understand why she drinks. I’ve tried and tried. I’ve confronted her 3 times about her drinking (the first time I wrote her a letter so it wouldn’t be as embarrassing for her) and each time I do it she gets extremely angry at me and refuses to speak. She threatens to leave, but I’m so afraid that if she did then she would seriously hurt herself. I’ve never seen a bottle of alcohol in the house (and I’ve searched).
The worst part is that, despite this situation, I have an extremely close relationship with my mom. But in my mind I just get so ANGRY and resentful at her sometimes, but can’t deal with it because she gets so offended if I speak to her.
I’m so afraid to leave home. I don’t know if she’s a legitimate alcoholic, or if her “bad nights” only occur after a bad day. My father completely ignores the drinking, and also gets angry if I bring it up. So, in turn, I’m resentful of him as well.
I don’t want to make this too long, but I also have found myself despising alcohol and I get really anxious if my friends or boyfriend gets drunk. I’ve never told anyone about my mother’s problem, so I can’t be honest to anyone about hating alcohol.
I feel so messed up. I feel like I’m the only ‘sane’ person in my house (other than my oblivious brother) and I can’t handle this anymore. I’m just so terrified that she’ll hurt herself and I’ll have done nothing.
What can I do for someone who REFUSES to listen? Is this what alcoholics are like?
There’s not a single person in my life that I trust with this kind of information. I have no clue what to do.