Yes, underweight people do stop getting their periods. Its very common in anorexia nervosa for example, and also generally when people are starved.

However you are 173cm and 63kg - your BMI seems to be well within in healthy range. But BMI is not perfect.

Regardless of the cause, it is not normal to stop having your period until you reach menopause. You should seek formal medical advice, not your family’s opinion. The very first question to ask yourself of course is could you be pregnant?