Is the questioner obligated to tell his cousin about his wife’s infidelity, or to cut ties with him, or what should he do to feel that God has forgiven him?

Do not tell your cousin what happened between you and his wife, and do not sever your relationship with him. Strive for repentance and conceal your sin, for the Prophet, peace and blessings be upon him, said: "Whoever commits any of these abominable sins, let him conceal himself with the concealment of Allah." Avoid the causes of sin and do not leave any room for interaction with that woman, even if it means refraining from visiting your cousin at his home. It is permissible for you to completely sever ties with your cousin if you fear relapsing into sin. We advise you to marry or fast, while guarding your hearing and sight.