I'm the same height and weight, but not the same age. I feel like my best weight is at 130. You are within BMI, but personally I feel pudgy at this weight.
Weight is not always a good indicator of how fit you are, and being healthy is more important than looking "perfect". Make sure that you are exercising regularly, eating healthy foods, and sleeping plenty. If you do these things, you will most likely gain more muscle and be healthier overall, which is great!
Muscle also weighs more than fat, so if you have more muscle you can be heavier. Exercise by doing cardio (running, swimming, mountain climbers, burpees, etc), arms (pushups, curls with weights, pull-ups, rowing, etc), legs (lunges, squats, squat jumps, adductors, etc), and abs (planks, curl-ups, sit-ups, corkscrew crunches, bicycle crunches, etc). Make sure you are eating all of the food groups -- fruit, veggies, dairy, protein, and grains.
Eat healthy foods when you are hungry, eat slowly, and stop when you are full. Sweets are also ok to have in moderation! I hope that helps!