How can one resolve the problem of a vow made in a state of extreme anger—to complain to a school principal—and then retracted for fear of sin?

Your statement: "I made a great promise to myself" has three possibilities:

1. Firm resolve: You intended to complain without verbalizing it, so there is nothing upon you. 2. Oath: You swore an oath to complain, so you must offer expiation for an oath (kaffarat yameen) if you do not do so. And whoever swears an oath and sees that good lies in abandoning it, then let him offer expiation. 3. Lajaj vow: You made a vow by saying: "If I do not complain about him, then I must do such and such." You have the choice between fulfilling the vow (if what you write is true and without injustice) or offering expiation for an oath.