I'm 5'5" and I'm 16 years old. I don't want any medicine. Is there any way to increase height by doing sports or by some diet?

Possibly. Depending on the status of your bone maturity you may have more growth possible or may be done growing. An x-ray of your left hand and wrist can be analysed for bone age, which is a maturity index.If it is more like a 14 yo then you have more growth potential than if it reads out 16 to 18. Balanced nutrition, rest and exercise are the basic needs for you to reach your full height.No sport or diet.