The relationship I have with my sister (age 9) is similar in some ways to yours (although less severe). Sometimes, particularly when we are both at home together for long periods of time, we really are at each other's throats. It used to be worse, but I have tried to change and this has made my sister change too.
The problem that I had with my sister was that, being older, I could be rather controlling. But of course, me being her sister and not her mother, she did not see me as an authoritative figure, and consequently did not respect me whatsoever. Because your parents are away, you are legally her guardian and because you are the older person in the house, probably take charge. I think her problem may be that she does not like to see you acting like this because you are not her mother but her sister. Consequently, she will not want to take orders from you and pretty much do the opposite of everything you say.
The actions of my sister totally drove me up the wall to the extent that I would be in tears at least once per evening, even if I was totally happy during the day. She knew exactly how to wind me up, and with her being my sister, insults and defiance coming from her affected me a lot more than they would if they came from somebody who I did not love so much. I spoke to my parents about this, and they said that while they could tell her off for being nasty, ultimately it was up to me to fix our relationship.
Since then I have tried to change my relationship with her by changing small things. When I speak to her, I try to use a calm tone of voice and ask things of her, not demand. I also try to set examples - if I do not want my sister to wake me up at 7am with the telly on too loud, I will not play the piano after she has gone to bed. By bringing this to her attention, it helps her to see that as i am being considerate, it would be nice if she could do the same. By gritting my teeth and not losing it, our relationship has improved. If your sister sees you deliberately being nice to her, involving her and setting an example, even when she has just been a little cow, she will slowly being to respect you and look up to you (however unwillingly on her part, it will happen!).
Another reason why you could be arguing is because she sees you as "invading her space". Since you have ben at uni all year, I expect that she almost feels like an only child - even though you are loved and not forgotten, with your absense the simple, day-to-day parts of her life will only involve your parents and not you. I don't really know what to suggest for this, but still it could be a perfectly legitimate reason as to why you fight so often.
Do not worry about sounding depressed - you just sound angry and want some help or at least an insight as to why your relationship is so bad.
You are not being selfish when you talk about leaving your family - it is totally understandable that you want to return to a place where you feel happier. And don't feel bad about your relationship "not working". Just because you love somebody doesn't mean you like them. If you want to get out, I would get a job of some kind. It means that you can be out of the house during the day, and even if it is just a till job in Waitrose, you will meet new people and have some time to think about your sister and other things without her at your throat.
Whatever you do, she will not change immediately. My mistake was thinking that if I was nice to my sister, she will be nice back. Because you have been fighting for so long, your sister will have built up years of resentment and "hatred" against you. But eventually, your relationship will change.