Is the questioner considered sinful for shunning her brother and not speaking to him, even though he is in the wrong and has not apologized to her, knowing the hadith: "It is not permissible for a Muslim to shun his brother for more than three days"?

It is not permissible to harm a Muslim without a legitimate Shar'i reason. Striking or cursing a brother is considered a sin and an transgression. It is forbidden for a Muslim to abandon his brother for more than three nights, and the better of two disputing parties is the one who initiates the greeting of peace (Salam). The greeting of peace, or returning it, removes the abandonment and lifts the sin. The majority of scholars hold that the greeting of peace severs the abandonment. Therefore, it is not permissible to persist in abandoning a brother.