All perfect praise be to Allaah, the Lord of the worlds. I testify that there is none worthy of worship except Allaah and that Muhammad, sallallaahu ‘alayhi wa sallam, is His slave and Messenger.
You did wrong by not throwing the pebbles on behalf of yourself and your mother, who delegated you. You are required to ask for the forgiveness of Allaah and turn to Him in repentance. As for the Hajj that you performed, it is valid. But each one of you is required to offer a sacrificial animal in Mecca, and its meat is to be distributed among the poor who live within the Sacred Precincts of Mecca. Throwing the pebbles is one of the obligations of the Hajj. So abandoning it requires one to offer a sacrificial animal. You have to tell your mother about that so that she may hold the intention, when the sacrificial animal is slaughtered, that it is offered as compensation for abandoning one of the obligations of Hajj.
If you were 15 years old at that time, then that Hajj clears you of your liability of offering the obligatory Hajj as you had already reached the age of puberty at that time.
Allaah Knows best.