I looked up the average weight for your height, and its 94 to 123. Girl (or boy) you are perfect. And if your family doesn't see that, then they blind as hell. So screw em, and throw the facts at them.
The smallest part of a teen's diet should be sweet drinks, candy, sweet foods, cakes, high-fat foods, junk foods (that's all one category). ( sorry if i’m wrong <3 ! )