I'm 13 5'1 or 5'2 and 117 pounds at the moment. I feel really fat and I don't know why. My mom always says that I'm not fat or I just have big bones or because I'm getting muscles from gymnastics! I eat a lot too. Can someone tell me if this is normal?

You are in normal range but you only have yourself to impress here so what you think of yourself is all that matters. At 13 and active in Gymnastics, you will build a lot of muscle tone  and lose a lot of weight over the course and remember you are the most beautiful person you know anywhere and don't let anyone tell you any different. Also in about 3 years, your body will undergo major changes  so be patient and enjoy life here.  Good luck