That is very normal. I was about the same at your age. At that age you are growing and your body is becoming more mature. As you get older the weight will regulize you don't have to worry it is not a problem
I'm 12 (nearly 13), about 5'5, and weighs 123 pounds. Is this normal, because I feel really fat? If so, how can I lose the weight?
Your weight is perfectly fine for your height.
you sound fine to me.
If you can maintain this weight all your lifetime....be happy. ..very very happy. The sounds like a good weight for you. That * fat* is just that you are developing womanly curves.