You are demonstrating symptoms of bulimia. There are better, healthier ways to lose weight that do not have long term negative impacts (messed up digestion, ruined teeth, poor relationship with food). Weight fluctuations are normal, especially if you're still on puberty, which ends around 21. It's also okay to like food!
Your parents (and probably others) are concerned about you and want to help you. You deserve better health and happiness that will come with a healthy relationship with food.
I wish you all the best in your recovery.