What should I do regarding my oath on the Quran not to marry anyone other than a specific young man, knowing that my family refused my marriage to him and I left him to please them?

This oath is binding on righteousness, and it is not broken unless you marry someone other than the aforementioned young man. In that case, an expiation for the oath becomes obligatory upon you. You have done well in pleasing and agreeing with your parents, for the Prophet, peace and blessings be upon him, said: "Whoever takes an oath and then sees something better than it, let him do that which is better and make expiation for his oath."