Ginger1776,
I'm so sorry you're having a rough time. First of all please know that we are all precious and we are all worth something or else we would not be on this earth. Sometimes I felt like I'm worthless. But I'm not. And neither are you, or anybody else. Not even the people who call other people 'worthless'. Everyone serves a purpose here. You aren't a failure. You're here for a reason.
Have you been spending time with your aunt? I think right now you should focus the most on spending time with her. I don't know what your relationship is like with her, but I would try to be with her as much as I could to make her feel a little better. Trust me... you don't even have to do anything. Your mere presence would be comforting to her.
Also, I'm very sorry about your friend who's in the hospital.
From what you've mentioned your sister sounds like she's acting very meanly towards you, especially with all those things you're going through. Right now I reckon the last thing you need is someone acting nasty towards you. I'd try to just avoid causing trouble with her for this period of time, until you feel better, which you will. I'm not saying cut your connections with her completely obviously. Just for this time, try not to supply any trouble.
You aren't being lazy. You're worn out. Give yourself time. What you're going through is more than understandable. You've been under so much pressure that it has overwhelmed you. Many people experience that. I understand.
I hope my advice helped, even if just a little. Please know that you are in my thoughts.
Hope things get better soon,
Burning Aroma