Is what is happening to me—this delay in marriage—a punishment from Allah because I sought divorce from my infertile husband, despite his good character? And must I marry anyone, even if he is not suitable for me, or is this a trial that requires patience? And what should I do?

A woman's request for divorce without a legitimate reason is forbidden in Islamic law, but it is permissible if the reason is the husband's infertility, because procreation is a natural and great purpose of marriage, and deprivation of it is a harm that justifies divorce. What you are suffering is a trial from Allah and His decree, not a punishment. Divorce may be a blessing, as Allah Almighty says: "But if they separate [by divorce], Allah will enrich each of them from His abundance." (An-Nisa 4:130). A divorced woman must choose her husband well, and the competence considered is in religious commitment. It is permissible for a woman to offer herself for marriage to one whose religion and character she approves, within Islamic guidelines.