For a 16 year old american girl standing at a height of 5 feet 7 inches/170.18 cm, is 114 pounds an okay weight?

Maybe,maybe not. At this body weight for height you have a bmi of 17.8 and fall into the bottom 25% of women in weight for height. If you are healthy and active and follow a balanced diet this is fine. Your predicted weight would increase into the 120 range within the next 2 years to stay in the same pattern.Failure to gain weight would likely place you in an under weight category.