Is it healthy for a 14-year-old girl who is 5'8'' to weigh 97 pounds if the doctor says you are normal but the BMI calculator says you need immediate medical help?
14 year olds should not use adult BMI charts as they are still growing. Your doctor knows you best and if you are healthy you are probably all right. Have you just had a growth spurt and are waiting for your weight to catch up? Are you a fidgety person, never still, always on the go? that will increase your metabolic rate and keep your weight down. In a country where the citizens are rapidly becoming obese with all the attendant health problems I wouldn't worry about being a little underweight, just eat a healthy diet, exercise and be thankful you don't have to watch the calories.