Irritated Easily

I'm the oldest (21) out of three sisters. The others are 19 and 13. The 19-year old is the mean one in the house and she somehow LOVES to pick on the youngest sister. I don't know why, but the mean sister is always picking on my youngest sister. For example, she'll tell her to pick  up her things off the floor, even if it's just one jacket hanging over a chair. She'll start shouting for her to pick up her stuff and uses more vulgar language towards her. Other times, she'll call her mean names behind her back and complaining about her to ME!  I'm always refereeing the two of them and it makes me sad to know that she will probably never get along with my youngest sister. Not only that, we go to school together and we have some shared classes. I sometimes ask to briefly look at her notes because I wanted to fill in some blanks at home and she always tells me, "Why don't you look at your own notes?!?" I tell her I needed to fill in some blanks, and she does give them to me after 2 minutes of nagging.

At this point, my parents and I think that something is mentally wrong with her. What's worse is that she is more book-smart and loves to argue well. She lacks emotional sense and street smarts and is so irritable all the time. (One time, she gave her driver's license number to some random person outside a building at our university, claiming she can register to vote after filling out the legit form. Luckily, nothing has happened so far.) Once you say something toward her and it annoys her, she'll start sassing you and you'll never hear the end of it. My parents and I think it's her hormones since she hasn't had a period close to half a year at this point. But still, I still have no idea what I'm going to do with her in the meantime.