You absolutely need more than 600 calories a day to survive long-term, avoid disease, and be generally healthy. Vitamins are not calories. You need more calories.
I understand that there is a lot of pressure, especially on us as girls, to be skinny and constantly be on more and more extreme diets. I'm glad you're on here and trying to do things the right way. That's why I'm on here too.
But just so you know, 600 calories a day is in a range that most people and mental health professionals would consider anorexic. A girl your size and age (I read your profile) shouldn't go under 1200-1500 calories a day. This doesn't mean you are insane or twisted or wrong, it just means you probably have bigger issues than your physical weight loss to deal with. Trust me, if you face those demons, the weight loss will fall into place. You don't need to check yourself in anywhere or be put into a hospital, but you do need to consider seeing a therapist or counselor. If you need any help finding one, please message me.
And for the record, you WILL gain weight when you start eating at a healthy level again.That is an unavoidable reality. But that's ok. Sometimes there are more important things than weight loss. Who cares if you gain weight? I guarantee you will still look better than if you were dead. And you'll still be at a weight many people would kill to be at. And once you get there, you can exercise your way back down to the size you'd like to be. At the very least try it and see if your body feels healthier.
