How can a person lose weight without creating a state of ketosis?

Ketosis is not necessary for weight loss.  Promoted by some low/no carb diets, ketosis is actually an indication that energy metabolism is not working as well as it could.  Here's a little science...ketosis is characterized by elevated levels of ketene bodies in the blood.  Ketene bodies are formed when the liver glycogen (the body's storage form of carbohydrate) stores are depleted.  We actually need some of this carbohydrate to completely metabolize fat -- so from a health and weight loss perspective it doesn't make much sense.

Explanation:

don't worry, but do consult a doctor.

explanation:

having a high metabolism at age 13 is not abnormal.   however, if you are concerned, do consult a doctor.   the doctor may identify a correctable issue, and then you'll have your answer.   in the meantime, there are a few steps you might consider.

first, reflect on just how much physical activity (work out and dancing) you are getting relative to your caloric intake.   keep in mind that if you are interested in gaining weight, you must have a higher caloric intake than output.   second, if eating robust healthy meals is not providing enough calories, you'll need to include high caloric, yet healthy, snacks.   i warn against using an over the counter high-calorie supplement (drink or food) until you have consulted a doctor.