Is the speaker considered sinful and deserving of God's punishment due to her feeling of dereliction in caring for her son, who died after being run over, given her suffering from depression and her use of psychiatric medications?

This world is a place of trial and tribulation, and one should not despair of Allah’s mercy. Rather, one must be content with His decree, Glorified and Exalted be He. The death of a child may be good, as in the story of Al-Khidr. One must be patient and seek reward from Allah for the loss of children, as Umm Sulaym did. Patience in the face of affliction brings immense reward in this world and the Hereafter, including entry into Paradise and the building of the House of Praise (Bayt al-Hamd). Negative thoughts, such as despairing of Allah’s mercy or believing that Allah will inflict upon you a punishment He inflicts on no one else, are whispers from Satan. Remember that Allah replaces the evil deeds of the repentant with good deeds, for His mercy encompasses all things. Therefore, one must repent sincerely and remain steadfast in obedience, for Allah forgives sins and guides to rectitude.