The truth of the matter is that God requires us to repent. This alone should be enough. Please, see the scriptures below.
Proverbs 28:13
13 He that covereth his sins shall not prosper: but whoso confesseth and forsaketh them shall have mercy.
Matt. 3:2
2 And saying, Repent ye: for the kingdom of heaven is at hand.
Luke 13:3
3 I tell you, Nay: but, except ye repent, ye shall all likewise perish.
Luke 15:7
7 I say unto you, that likewise joy shall be in heaven over one sinner that repenteth, more than over ninety and nine just persons, which need no repentance.
Acts 17:30
30 And the times of this ignorance God winked at; but now commandeth all men every where to repent:
2 Corinthians 7:10
10 For godly sorrow worketh repentance to salvation not to be repented of: but the sorrow of the world worketh death.

This is largely my personal beliefs based on my experience, so please, take it with a grain of salt. However, I hope it does elicit thought and prayer.

I have found that when I do things wrong, especially those that hurt another, I hurt and I carry an all to real burden. Just ignoring it doesn't cause it to go away. With me, it often time amplifies it and causes major problems in other areas of my life.

Repenting can be a huge relief and a major part of healing. Whenever I repent, I find that I suddenly feel much lighter inside. My back doesn't feel like it carries such a load anymore, as well. Even better, there have been times where the sins have hurt myself, or caused others to hurt me. When I repent, I can feel myself start to let go of the anger, pain and hate associated with the sin. You might argue this is the healing that happens as you forgive yourself. It might be, but in the process of repenting, there is that healing as well.

• Recognize What You Did Is Wrong
• Feel Godly Sorrow
• Stop Doing It!
• Confess (to the wronged party and, if necessary, a High Priest)
• Make Restitution
• Never Do It Again
• Forgive Others
• Forgive Yourself

Obviously, you will want scriptures for this. Here are just a few:
2 Corinthians 7:10
10 For godly sorrow worketh repentance to salvation not to be repented of: but the sorrow of the world worketh death.
Acts 26:20
20 ... that they should repent and turn to God, and do works meet for repentance.
Doctrine and Covenants 58:43
43 By this ye may know if a man repenteth of his sins—behold, he will confess them and forsake them.
Numbers 5:7
7 Then they shall confess their sin which they have done: and he shall recompense his trespass with the principal thereof, and add unto it the fifth part thereof, and give it unto him against whom he hath trespassed.