Please see a doctor, first and foremost. It is good to have solid, reputable medical advice on this journey AND accountability. A doctor will keep track of your progress for you.
Then, get rid of your scale. Burn it. Run it over with your car. Drop it outside the window. Whatever you have to do.
Drinking water will not make you gain weight. You know that.
You need water. You need to gain weight. When you stop getting your period, it is your body telling you something is wrong. You only have one body. It doesn't know what being "fat" or "ugly" is. All it knows is that it is not getting enough nutrition to perform regular, healthy functions like menstruating. Our lives are so short and so precious. You are young and need to be enjoying this time. Please, please treat your body well.
Obviously you know you have a problem here and you know what needs to be done. You have to eat (gasp!). Food is sustenance. Food is what brings people together. There is no reason to deprive yourself. A 2500calorie(or more)diet, without exercise, is reccomended for recovery. Best of luck.