Are the accident that befell my mother and me, and my lack of success in my studies, due to my writing an offensive word about the teachers on the school wall, and my mother's denial of my presence at home when they summoned me? What should I do about this, and what will be my recompense in the Hereafter?

Whoever harms his female teachers by assailing their honor or speaking ill of them has committed a sin. Likewise, denying your existence is a forbidden lie. Both of you must repent immediately by ceasing the sin, regretting it, and resolving never to return to it. If the matter involves the rights of individuals, then it is obligatory to restore those rights or seek forgiveness. Some scholars have said regarding backbiting and similar sins that seeking forgiveness for the person and mentioning their good qualities in the gatherings where they were slandered is sufficient. The calamities that have afflicted you may be due to sins or the prayers of the wronged, and every calamity that befalls a person is due to their sins, and Allah expiates sins thereby.