Yeah, the throat thing will pass. Go to your local health food store and buy some throat coat tea -- it'll help soothe it in the meantime.
Family dramas are horrible. Sorry to hear that. Tell your sister that you need time to yourself to sort through some things and "reflect" and that you will get back to her when you are ready. If she can't respect that then tell her she's the one with the attitude and needs to think about others' feelings besides her own. I would not panic about the voice thing, sounds like you strained your voice box, so it will likely heal up (if you don't talk much or project your voice) within a week or so. If anything, write on a piece of paper or email the harassing sister that your voice is out so guess you can't talk to her for now. What a shame that must be! ;-)
Worrying comes to normal people, that is, people who don't suffer from chronic anxiety or depression, from not doing something about a festering situation. Anger is natural as long as it doesn't lead to violence, so why not have a conversation with your sis, agree you both were angry, and accept you'll have differences. Hopefully, you can accomplish something that way and stop the worrying and move on.