How about any relatives that you could possibly live with temporarily? Try to reach out to any supports in your life and see if you can set up a temporary living situation. I know you don't want to live with your BF right now but perhaps if it's just temporary it could work? It sounds like even though it's not the ideal option, it might be an option to help save your sanity in the meantime. Even if you don't physically shack up with BF, at least maybe spend 90% of your time with him vs. any time you would be spending at home?
I completely empathize with your situation and know that you're not getting any of your emotional needs met. Try to utilize other supports and realize that your mother is just not going to be high on that list of support while your sister is the way she is. I would say that in this case your sister is so unstable that you really do need to get out at any cost. Whether it's drugs or mental illness along with her medical issues, it's not good for you. I'm sorry you feel stuck, but please consider all other options to get out of that household.
Good luck.
Also, here are a few resources on this page for your state - call the information and referrals # listed first to see if you can get some sort of counseling through the state:
http://www.state.nj.us/humanservices...ttinghelp.html