What should I do about my sin of adultery and my wife's illness? Will my Lord forgive me for this sin? And will my suffering continue, or will my situation change?

One must repent to Allah Almighty from the unlawful by abandoning it, regretting it, and resolving not to return to it, while concealing one's sins, striving in good deeds, and frequently remembering and supplicating Allah. No matter how great the sin, Allah's forgiveness is greater. He accepts repentance, rejoices in it, and replaces bad deeds with good ones, as He states: "And He it is Who accepts repentance from His servants and pardons sins, and He knows what you do," and His saying: "Say, 'O My servants who have transgressed against themselves [by sinning], do not despair of the mercy of Allah. Indeed, Allah forgives all sins. Indeed, it is He who is the Forgiving, the Merciful.'" Repentance wipes out what preceded it, and the one who repents from a sin is like one who has no sin, and will not be punished in this world or in the Hereafter.