You might talk to your counselor about this. I hope you could take a piece of fruit and a small sandwich
for lunch. Do you eat a a fairly big breakfast? That might help you get through the day. You can always have a small bag of nuts for protein. I don't think soda is good either. So maybe some nuts a bananna and some crackers like Triscuit would keep you going during the day.
You are too concerned and you need to at least get a snack from time to time during the day.
The thing about starving all day is makes you not want anything when you get home. We all need to keep up some intake of food so we can think and work on things at school.
Maybe your counselor will have an idea for you to get what you need for your situation.