Just an observation- Maybe your sister is in denial; she recognizes symptomatic things about herself in you and it terrifies her and she has no resources to get help.
No suggestion about interacting with BF, having never had one. Perhaps sleeping is a way to escape the reality of what is happening to you and his feelings of inadequacy in helping you? It sucks to feel powerless to help someone.
I am the last surviving member of my entire family, I know what the mounting loss feels like when there isn't time to recover from the previous one.
At one time my elderly father was pressuring me to move him in with me, truly a cosmic joke since we had barely tolerated each other since I was a teen. Suddenly he found he had nobody who could stand to be around him. He was cranky, in failing health and strength, smelled terrible, and was violently shorted tempered. I refused to take him in. When he died, I was the last. I hope your situation isn't as bitter as mine was, I wouldn't wish it anybody.
To be honest, relationship things are my weak point since I had such poor familial examples as I grew up. I wish you the best from the bottom of my heart but feel useless in suggesting working solutions.