Why did God want an infidel girl, who spent her life miserable and full of illnesses and problems in this world, to be tormented in this world and the hereafter?

Tribulation in this world is common to both the believer and the disbeliever. In fact, it is more severe for believers because they receive multiplied reward, while the disbeliever deserves punishment in the hereafter for their disbelief and evil deeds. Allah wrongs no one.

People are of four types in this world and the hereafter: one who is given abundance in both; one who is given abundance in this world but limited in the hereafter; one who is limited in this world but given abundance in the hereafter; and one who is wretched in both.

There are six types of deeds: two that are obligatory, namely Paradise for whoever dies as a Muslim, and Hellfire for whoever dies as a disbeliever. Then, there is "like for like": whoever intends an evil deed but does not do it, it is not recorded; but if they do it, one is recorded. Then, "tenfold": for whoever performs a good deed. And "seven hundredfold": for whoever spends in the way of Allah.

Allah may hasten for the one who desires this world what He wills, not what the servant desires. And He may deprive the one who desires this world from it, thus causing them to lose both this world and the hereafter.