Firstly- this is NOT your fault. Your mother's choices were made by her- NOT you. You're a child and your mother is the one that has the problems. She can't face-up to her part in them, so she blames you. You're a safe person to blame things on; she knows you won't walk away & you'll take what she throws at you.
The bravest thing you can do is what you're doing- Reaching out for help.
Secondly, you're very young, so I know that you can't walk away. You're at the stage where you will do everything to get her off the drink, whether it's pleading, contacting doctors/authorities or- as is in your case- take the blame for her behaviour.
I'll repeat this, because you need to know it & ingrain it in your memory: Your mother's addiction is NOT your fault- it's her's. She can choose whether she drinks or not.
And you cannot make her choose sobriety.
There are complications with long-term alcohol dependency. Usually, it's extremely hard for alcoholics to completely stop drinking. They go through quite severe physical withdrawals and can put their health at risk by going cold turkey. Your mother would need to be under a doctors supervision & would possibly be advised to cut down gradually.
However......the first step in all of this is for her to realise she has a problem.
This is not something you can neccessarily do, but I have a few tips for someone in your situation & I hope they are useful.
*Your mum's drinking is down to problems in 'her world' that don't concern you & your sister. They are issues that have probably built up over a number of years & possibly issues that are as deep-rooted as childhood. She is clearly an unhappy person & while you & your sister are suffering, she is also a victim of sorts. She is a victim of an addiction. Remember this when she's screaming at you & being horrible- it's not her; it's the person her addiction makes her.
*Don't try & have a serious conversation with her while she's drunk/drinking. If possible, pick a time that she can't/doesn't drink & talk about her behaviour/addiction when she's sober. And if possible, present her with evidence (drunken photos, videos, etc). This is the shock tactic; showing the alcoholic, the true extent of their drunken behaviour with evidence to back it up. It's a hit of embarrasement.
*If/when she starts ranting- try your hardest not to react. Let her say her thing & say nothing in retaliation. When you think she's finished, hit her with emotion, eg; "I love you, mum, but I like you more when you're sober". Keep it simple & walk away (don't stomp, march, etc- just walk slowly & casually away).
*Recruite friends & family to speak to her too. BUT don't all do it all at once- each do it when spending time alone with your mother. If she has a crowd of people telling her she's in the wrong, she'll turn to drink to escape the feeling of persecution. And if possible, contact a local alcoholics anonymous group. They don't only help the alcoholics themselves, but can offer help & advise to family members. I can't give you a website address, because I don't think they're allowed on here & I don't know where you are!
Good luck & I really hope your mum sees the light soon. Keep strong & keep believing that, one day, her behaviour will be a bad memory.
Hugs to you.