Jesus told the parable of two men who went up to the temple to pray (Luke 18). The Pharisee didn't care about any sin at all, he thanked God for being so much better than everyone else. The tax collector, crushed by his conscience, wouldn't even lift his eyes: “God, have mercy on me, a sinner.” Jesus concluded: this one, not the other, went home forgiven.
It's Proverbs 14:9 told as a story: the fool mocks making amends for sin; goodwill is found among the upright. And the great surprise of the Gospel is that the “upright” isn't someone who never sinned, it's someone who runs toward forgiveness.
But wanting to be forgiven wouldn't be enough if no one had paid the price. That's why Christ went to the cross. The forgiveness your conscience is looking for has already been bought with His blood: “If we confess our sins, he is faithful and just and will forgive us our sins and purify us from all unrighteousness” (1 John 1:9).
The worst deafness is a numbed conscience; the greatest grace is a heart that still cares and runs to Christ. Don't pretend everything's fine, bring your wrong to Him, because the forgiveness is already paid for.