How can I lose a few pounds?

I’m 13, a girl, about 120 pounds, five foot three, and want to lose a little weight. I’m tired of feeling uncomfortable in my body no matter what I’m wearing, even though I’m not overweight. Every time I try to eat a salad I literally gag, and don’t want to force myself to eat something I absolutely hate. I try to eat healthy and eat less, and exercise for about an hour at least three times a week. People say I look good but I just don’t feel good. All my friends are skinnier than me ( yes, I know they haven’t gone through puberty yet but it still makes me feel bad ). I want to lose maybe ten pounds, but don’t know how. I have an injured wrist, so that makes it harder to find exercises I can do without it. My diet is pretty good. I try to stay away from candy, sweets, fast food, sodas, real fatty foods, and that stuff. I try to drink a lot of water everyday and no more than two cups of milk because it makes me break out if I have a lot.
I have started running/walking a few times a week for about thirty minutes at the most. (I’m very out of shape right now). I also jump rope about once a week for around ten minutes off and on.
So, what else can I do to lose ten pounds quick and get in better shape? What should I eat and are there any exercises you know of that burn a bunch of calories?
Thanks.