I'm underweight and i exercise: how can i gain weight?

As a former swimmer, I find it hard to believe that you have a weak core. Unless you don't do any freestyle or your form is just terrible, you probably have a better form than most girls your age. However, if you make sure to eat a large amount after you are done with physical activity for the day, say around 8 pm, then those calories will not be burned off. If you are really concerned, you can see a nutritionist or go to a store for some weight gain formulas, but they can be pretty pricey.