What can a repentant, remorseful young man do to rid himself of the constant remembrance, fears, and shame stemming from his previous attempt to commit adultery, knowing its severe prohibition?

Allah is Forgiving and Merciful, and whoever repents of a sin with sincere repentance, Allah will accept his repentance and forgive his transgression. The repentant person returns as if he had no sin. He should have a good opinion of Allah, and frequently make supplications and humble pleas to Him. Remembering the sin is sometimes beneficial. He should also increase in performing good deeds, for indeed, good deeds efface bad deeds.