Be careful what you do. If you diet now while your metabolism is high and you are young, you can lower the amount of food your body will feel it needs before storing fat. You can also make yourself very unhealthy. The best way to lose weight at your age is to make sure you walk briskly or exercise for about an hour every day, and to make sure you eat 6 to 10 servings of fruits and veggies every day. This will make you feel fuller so you can focus on eating less junk food, candy, and fatty food. Although a little bit of fat everyday from healthy sources like nuts, peanuts, fish or olive or canola oil is very very good for you.
I am the same height and weight as you, and I am 33. I am not skinny, but I am not considered fat either. My husband thinks I'm gorgeous and I get compliments on the bus once in a while and not usually from creeps! This is embarassing but nice in a way, and I know that even though my BMI is over 25, I am more muscular and strong than the average woman and I am not obese.
I know from past years when I was sportier or cycling more often that when I get fitter (the hour - even in bits is fine - of brisk walking/jogging/biking daily), I stay the same weight but my size goes down because I am losing fat and gaining a little muscle. At most I lose 10 pounds over a year.
So, my advice to you is don't look at the scale, look at how your pants fit, and how healthy your diet and lifestyle are. If you excercise you will also have a lot more energy, and make it easy to stay fit later in life when you are a lot busier with grown-up responsibilities. Don't worry about looking like a supermodel - when you are my age you might be a little bigger than you are now, but so will everyone else, and if you take good care of yourself, the difference will be small. You will keep growing and developing until you are 25 or so, so don't stress out - you will grow into yourself, and change all your life. Also, most people who are good partners and friends don't care if you are perfect looking, and find healthy very attractive!