Must a girl who has never experienced the white discharge or dryness before, and used to perform ghusl and pray on the tenth day of menstruation in accordance with the Shafi'i madhhab, then began to see the white discharge on the thirteenth day, now follow the madhhabs that state a longer maximum period for menstruation?

Perhaps you meant to follow the Hanafi school of thought in your ghusl on the tenth day, because they hold that the maximum period of menstruation is ten days, while the majority (jumhur) hold that the maximum period of menstruation is fifteen days, and this is what is given as fatwa (ruling) by us. Based on this, as long as you observe purity on the thirteenth day, all those days are considered menstruation. And there is nothing due upon you for what has passed, as long as you acted according to a valid opinion among the sayings of the people of knowledge.