My mother thinks I'll mess up my exams if I fast. If i do fast on exam day, she might get extremely angry at me and also worried. Yesterday she explained it might affect her health if I do fast because of how worried she will be. Should I obey her or fast on that day?
You are not required to obey your parents in sin. If fasting is prescribed for you (i.e: you have no significant health complication, you are pubescent, you are not menstruating etc) you should fast.
Your mother will learn to accept it once it becomes normal for her, remember that people used to fight wars while fasting.
Fasting is the most important obligation of Muslims and they have to fast. But in your case if you are adult and having fast is obligation on you then you have to fast no matter its your exams time or any other important task. You should fast and also try to get good grades in your exams so your mother will be satisfied and will not consider fast as a burden or any other mess for your exams. And you should also satisfy your mother by telling her that you Islam as our religion comes first and first we have to fulfill all obligations of being a Muslim. So provide her a comfort zone and then she will remain calm and would not be worried about you.