Hi Summer01,
I'm sorry you are having to deal with your difficult sister and her spilling the beans all over facebook Unfortunately, you can't control what your sister does you can only control what you do.
I would suggest ignoring what she's throwing out there. The people who know and care about you won't believe it or listen to it. If she is "drunk" or an alcoholic many people have probably witnessed that and would take anything she says with a grain of salt and finally if you JADE (Justify, Argue, Defend, Explain) you can end up validating what she's saying. You don't want to validate the invalid. I know it's hard not to respond, it's natural to defend ourselves or want to tell our side of the story but your sister is using this stuff to bait you into engaging in drama with her. Fear of abandonment is at the heart of BPD and unfortunately engagement even negative engagement helps assuage those fears.
For example... .say she posts something... .Summer01 wore her panties on her head all of fourth grade!

If you react and start posting no I didn't, you made that up, you didn't even go the the same school as me in fourth grade people might wonder why is Summer even responding to this? Is there some truth to it? (Summer doth protest too much) I know this is hard particularly if she is posting truths and partial truths.
You are not alone in the pwBPD in your life badmouthing you, over sharing information or outright lying about you. Like I said above the people that really matter won't buy into it, and what many of us find is that the people who buy it initially eventually figure out that what is being said probably isn't true.
Since you can't change what your sister is doing, what can you change that you are doing? Can you stop reading her Facebook posts? If you find it difficult to do that on your own, can you block her on Facebook so you simply don't see her posts anymore?
In terms of your relationship with your sister do you want to continue your relationship with your sister at this time? Knowing what you do about your sister's behavior how do you realistically envision a relationship with her? There are lots of options, you like your mom and other sister could go no contact, you could just take a break for a certain amount of time, you could go low contact say communicate only via email or 1 phone call a month or whatever works with you, or you can learn more about BPD and learn some skills that might help in your current relationship. Also, know that what you decide to do now doesn't have to be set in stone forever you can always change your approach as your situation changes.
Welcome to the bpdfamily I'm glad you decided to jump in and post and I know the members here will have some great suggestions, ideas, tools and support to offer you.
Take Care,
Panda39