I live in North Carolina! Even if I know it's such a large place, I can't help but wonder if I know her!
Buuut I guess I kind of understand. There's two generations of kids in my family: the ones near my age, so finishing up high school or somewhat fresh out of it, and then there are the little ones that are either starting middle school or still in elem. Luckily for me, I've known my cousins forever, so I can sort of get along with them. My only female cousin (well, the only one close in age to me) and I get along pretty well, even if we're nothing alike. She's all tall and graceful and popular and really into shopping and make-up and has tons of boyfriend (not all at once!) and cool. I'm just kind of...awkward and nerdy. But she and I get along pretty well, bonding over the fact that in our generation, we're the only females—and born in July. (There's about five guys, both older and younger, so they all pretty much picked on us a lot, at least until we learned to fight back—physically.)
But there has to be something in common. Perhaps a film or a piece of clothing or song or a book or something. Try to think back on it, or perhaps ask one of your parents about her. Or just learn a little about her and talk about what she wants, and perhaps try to find a way that it connects to you. Just do a little research and I'm sure you'll be fine. And so what if what you like is not up to her taste? It's YOUR style, not hers. If she doesn't like it, shrug it off. You know she makes fun of you, and you make fun of her, so there's really no reason to get sad about it. Just roll your eyes and get on with your life.