Firstly, I am really sorry to hear about your mum's death. I know that must be a very hard thing to go through, and you must miss her terribly. Try and stay strong. Did you and your sister get any form of counselling after she died? I'm thinking there is a lot of emotion there, both on your sisters side, and on yours, and she doesn't know how to handle it. She's basically 'lashing out' at anyone who is closest to her, namely you. I doubt she means it, if she's implying it was your fault. She just doesn't know how else to deal with it.
Do you have an older relative, your dad or a Gran maybe? Someone you can explain what's happening, and let them have a chat with her. It's possible she doesn't realise she's doing it, or she doesn't know how else to cope, and they can help with that.
Whatever you do, don't take blame. Accidents are exactly that, you can't change it, or go back. It's cruel but it was meant to be, obviously. You now have to get on with your life and not let this hold you back, she will want you to be successful and will always be around you