I'm chiming in late here, I hope that's ok, but I just wanted to say how much I empathise with how complex this situation is for you on so many levels. Yes, of course all of the pragmatic advice about having the right to simply say no is good advice and very very true.
But I also know that it can be extremely difficult to pull off in reality and is sometimes a stressor in itself that can feel worse than the thing you are trying to say no about. And with the added complicating dynamics of the serority (which I admit I don't really understand but can imagine are very binding and significant), I think you are wise to give this lots of consideration with an eye to all possible consequences.
I agree with KP, I really do. "Whatever gets you there" is my favourite motto sometimes. If that means lying, enlisting the help of a co-conspirator, telling the truth and hoping for the best, strategically arming yourself with a single drink that *miraculously* never runs dry throughout the evening, or whatever else, then do it. You owe nobody other than yourself anything, and to yourself you owe the greatest care and respect that you can. Sometimes doing "the right thing" is just about what's right for you.
As someone who used to drink heavily in social situations for the sole purpose of conquering my social phobia and extreme inhibition, and who now can't dare to do so because of an inability to manage PTSD symptoms, I can attest to how hard it is to find a new social self and context that feels safe and ok. It's actually a really big deal personally, no matter what anyone says.
I really deeply empathise with you. Ideally, an understanding sister within your group who could keep an eye on you, help you to manage and divert drinks, help buffer you with the other girls if explanations are required, etc, would be ideal. Do you think there is a chance that such a person exists in your group?
Maddog