OK, I got mod-smacked last time I expressed my entire opinion of a kid, so I'll tone it down this time:
Your mother is right.
She is making parenting decisions for her young child (and I mentor kids your age. You may feel like Mr. Big Man, but you are very much a child.) The rating systems exist for a reason, and I don't think I'll get too much pushback if I say that as a general rule gamers (at least gamers over 17) understand and appreciate that rating system as, when it's used properly, a very effective means of keeping the Jack Thompsons and Michael Atkinsons of the world off our asses.
You're trying to use your IQ and your grades as a sign of maturity. Nice try. My IQ's high enough that (oh, fuck it, just find that other thread about IQ and read my posts there), and when I was 13 I was so immature that it's debatable whether I had any business playing T-rated games (I got better)!
Your lack of maturity shows through not by you having the more stereotypical (grades, drug problems, etc) signs of immaturity in kids your age. It shows in your inability to understand the problem from the point of view of your parents.
Furthermore, I'll throw in my own two cents here---if you need violence to feel better about games, maybe you shouldn't be playing them! If you're "not violent at all" (your words), then what do you need that for? Maybe you should discover something that might better fit your soi-disant "nonviolent" nature.
Try strategy gaming. Simulations. Abstract wargames, even. You might find something much better-suited to your gaming needs that also happens to be parent-friendly and everybody wins.
And really whether you like it or not you are under your parents' authority and more kids these days need to learn basic respect for their elders (like I said, I mentor kids your age, and thankfully they're really good around me, but I'm not so naive as to think that at least a few of 'em aren't total dipsticks when they're not around the guy who's teaching them financial literacy---my mentoring program---and telling them they can get rich someday and buy awesome stuff.)