Ok, well if it's your family you need to sit them down, either individually or together, and explain just how much their words and actions are hurting you. All families have arguements and snipe at eachother but it seems like yours in ongoing and that it is havng a lasting effect on your health. I'm sure they love you - like I said, people are sometimes so wrapped up in their own worlds that they can't see the dammage they are doing to others. If your sister is ill then it is understandable that there is strain and tension but you shouldn't be the one it gets taken out on.
Of course you can't control how you feel but you can control your actions. Hurting yourself is not going to make things better. You need to change the attitudes of the people in your family towards you. Why do you think they pick on you? I know sometimes it can be done with no reason but maybe if they explained certain things that you do that cause them to shout, you could stop. And, in turn, you can explain the things they do that make you want to hurt yourself. If they are reasonable people and they care for you, they should be able to make the change.