When I was 13 I was huge [I hide all pictures from that year] thing is, when I turned 14 I grew two feet [I was always the shortest in my class] and everything evened out. So, don't worry too much. If you do pick up a diet and exercise routine, try and do it for other reasons beyond being thin. If you're mentally beating yourself up you will have a harder time losing weight, do it for personal reasons. [Looks isn't a bad thing, but it shouldn't be the only reason, it's very unhealthy]
You should work on overall weight loss since you cannot target an area, so start with cardio [get proper shoes! Trust me] you could start with long walks, then work your way up to jogging and running. Try interval training, walk 5 minutes, jog 2 minutes, walk 5 then work your way up to jogging/running longer. [Also, warm up and stretch when you're done] you can also try weight training after a while to tone [Look into squats, pushups and things you can do at home] leave the core exercises until later, muscle will build under any belly fat so your belly might poke out a bit more. Try taking measurements along with your starting weight, and check once every week or two. You may not loose weight, but you'll tone and certain parts of your body would get thinner.
Food wise, eat more fruits and vegetables, lean meats, whole grains. [Look into portion sizes] try to fill your plate with vegetables too. If you can, try finding a free app to help you with calorie counting. Figure out how much you need and cut out 200, carefully not too much since you're still growing, but also too much will put your body in starvation mode and it will store fat. SparkPeople is a good one since it also tracks your water, food, and the calories you burn through exercise. [Not sure if it's an 18+ app but it's free]