It would help if you told us what your current diet is. You will need to change your diet dramatically if you eat like a typical 13 year old. Cut out the junk food, fast food, and the sodas. Drink lots of water during the day. Try for 1 gallon per day. Eat smaller meals more often. You should eat 5 to 6 times a day. Eat healthier. Instead of grabbing a bag of chips, eat some carrots. Instead of going to McDonalds, grill a chicken breast or eat tuna fish.
The other secret is exercise. Get out and walk for a half hour each day. You can buy some exercise videos to do at home. You can buy a cheap set of dumbbells and start weight lifting at home. It does not cost a lot of money to exercise. It helps you lose the fat and keep it off. Not only that, but you will get a ton more energy from it.
Also remember that you are still growing. 50 lbs in 5 months is a good healthy way to lose weight for an adult, but for a growing teen, it may be too much to lose. As you grow, you will be gaining more lean body weight. You may also add some extra body fat. Don't be too concerned about it until you are fully grown. If you start a too drastic diet, you may deprive you body of some of the nutrients it needs to grow. But if you eat a good, healthy diet and exercise, your body will get all the nutrients it needs to grow and you will be on your way to looking great. And if you get in the habit of eating right and exercising at your age, you will not face the problem I am in your 40's.