You aren't fat. You should eat wheat. Whole wheat.
People need gluten unless they have celiac disease. You don't need to lose anything. Instead of cheating and eating a lot, focus on making sure you have healthy stuff you like every day.
Plan on one tiny desert a week so you don't feel deprived.
Or are you taking any new medicine, some medicines have a side effect of weight gain. Also, that's not that bad, 129 pounds isn't fat. I have a friend who is 12 and she's the same height as you and she weighs 140.