You may know this because of your sister but there is no specific emancipation laws in your state. There's no statute for emancipation of minors. South Carolina doesn’t have an emancipation statute that specifies an emancipation process. However, it’s possible to petition the juvenile court to get yourself legally emancipated.
You would have to show several things -- that you have the ability to be self-supporting, so your good job is going to be important. You have to show that you have a place to live (your sister's) and you will want to show that your sister went through the same thing which will help when you explain that there are emotional issues at home.
You may want to wait till you're 17, but you don't necessarily have to if you're mature and have a good, steady job. It may be more easily granted if you're 17 than 16, so that's why I'm suggesting that. In many states, a 17 yr old is more easily emancipated than a 16 yr old. While your state doesn't have a statute, it's just a suggestion. If you want to become emancipated now, then you will need to show pay stubs, show how you're doing in school unless you dropped out (and if you didn't, I would suggest you stay in school because it will matter later on). You can file a petition at the juvenile court in your county and then the court will likely schedule a hearing for you.
You can do this yourself and if indeed you can do this yourself, and argue in your own behalf, you show the judge that you are mature and that you can handle this tough issue yourself.
Is there anything else you need or want to know about this?