How csn I gain 15 pounds im 19 female 5"3 and only 98 pounds?

Gain some weight! The one factor i need to know to properly answer your question is what your activity level is. We can assume light activity and come up with a rough estimate. Your BMR is about 1300 calories/day and your daily calorie needs assuming light activity would be 1, 770 calories, if you assume moderate activity it would be about 2, 000 calories. You need to eat more than your daily needs to gain weight!
Consume calories. It is possible to gain more weight by consuming more calories then you expend. What you want to be careful about is gaining the right type of weight. You would typically want to gain muscle weight, more than just fat. Please consult your pcp to make sure you have no underlying cause for low weight and he/she will be able to guide you to a proper exercise program as well.