I have a clingy friend?

So i made a new friend at gym class! But she's soo clingy! I've asked my other friends if she's like this around them too, but they said that she's realllyyy shy and they've never even heard her speak. At gym class she demands to be right next to me. No..seriously..shoulder to shoulder. I don't mind, but she has bad hygiene! omg i could smell her unshaved Pitts. And if the teacher splits us up into different teams, she gets really comfortable without me by her side. ooh and suddenly, to her, we look alike. "twins" she says. But really we don't, not even close. She's kind of annoying, like we'll be playing a game of volley ball at gym and she would just stand there talking non-stop about her long distance relationship with her "boyfriend". I'm a competitive player, shes all up in my zone when I'm aiming for the ball lol. She's all over me, i have no space! and in the locker room she wants to share lockers with me?? nooo! OH and now she calls me "boo boo". theres not one second during my gym class where she's not hovering over me. I don't mind being her friend but i met her about 1 week ago and she claiming me as her best friend. My current best friend doesn't like her at all. And drama is the last thing i want. Speaking of drama many people that i know have told me that she's a self harmer. i looked at her wrists today.. no scars. But when we were changing into our gym clothes. i saw her legs and almost cried. when i asked her what happened she said "my cat" I don't wanna be mean and tell her to leave me alone. She seems so fragile ... this is serious, i don't know her story, i don't want to say something and hurt her. whhaaaat shoooulldd i dooooo??