In the past, because I had heard the phrase "the confession needs to be as public as the sin," I became very busy spending much time thinking of times I had sinned in front of others. I then would write them a note, message them, talk to them, etc. about what I had done. It really was a revolving door and not much really was accomplished by this, I think. In fact, sometimes I think more harm than good was accomplished.
But every time I wrote a note or mentioned it I said, "since the confession is supposed to be as public as the sin ..."
Now I know that that is a false statement. Should I got back to everyone I confessed these sins to and confess to them I was wrong about it? I will do it if God's Word seems to point me in that direction, but if not I would rather not. It will be a lot of work, and some people I don't even talk to anymore.
Do you know what I should do in a situation like this?
It seems to me that you are caught up in thinking that in order to be forgiven, you have to confess every sin to every person you sinned against. The problem is that there is no passage that states that. We are to confess our sins to God. "If we confess our sins, He is faithful and just to forgive us our sins and to cleanse us from all unrighteousness" (I John 1:9). We are also to talk to brethren who can guide us, support us, and pray for us. "Confess your trespasses to one another, and pray for one another, that you may be healed. The effective, fervent prayer of a righteous man avails much" (James 5:16). Nowhere is there a teaching that a confession is to be as public as the sin. Nor is there a requirement that you must confess to everyone you sinned against in order to be forgiven.
When you repent of a sin you change your attitude toward that sin and your behavior. "For observe this very thing, that you sorrowed in a godly manner: What diligence it produced in you, what clearing of yourselves, what indignation, what fear, what vehement desire, what zeal, what vindication! In all things you proved yourselves to be clear in this matter" (II Corinthians 7:11). The change should be so complete that people in the future would never guess that you used to sin in that manner in the past.
A part of the change means not profiting from past sins. That is why Zacchaeus said, "Look, Lord, I give half of my goods to the poor; and if I have taken anything from anyone by false accusation, I restore fourfold" (Luke 19:8). Zacchaeus declared that if he wrongfully took money from someone, he would return to that person four times what he stole. The Jewish Law only required that a thief return 20% more, but we can see Zacchaeus' zeal in wanting to change because he was willing to do more than the law required. Of course, there would be many whom Zacchaeus would not remember or not able to restore. For these, Zacchaeus declared he would take half of what he had and give it to the poor. Perhaps those he stole from would benefit, but in this manner he removed the ill-gotten profits from his own household.
Another part is repairing the damage caused by our sins. If someone has a grudge against you because you sinned, then you need to let them know that they were right and you were wrong so that they have an opportunity to forgive what you did. "Take heed to yourselves. If your brother sins against you, rebuke him; and if he repents, forgive him. And if he sins against you seven times in a day, and seven times in a day returns to you, saying, 'I repent,' you shall forgive him" (Luke 17:4-5). Notice that the one who was wronged is taking an active part in trying to get the sinner to change.
This is not the same as doing something wrong that others don't think is wrong or don't care about. In such a case, you still need to change to no longer be doing sin, but there is no reason to chase people down who never thought about your actions. If you do happen to run across someone who brings up a past wrong, by all means apologize and tell them about how you realized it was wrong and changed.
If you caused harm to someone because of your sin, then if you can you should try to undo the damage. But in your case, you misspoke because at the time you misunderstood what was right. You've changed and now no longer say such a thing. For most people, they probably don't remember what you said. If you run across another person with the same wrong idea, then you can discuss why it is wrong and help them see the truth.
Don't think that forgiveness only comes with perfect correction of each sin because such will never happen. You do what you can and then leave the past behind. "Brethren, I do not count myself to have apprehended; but one thing I do, forgetting those things which are behind and reaching forward to those things which are ahead, I press toward the goal for the prize of the upward call of God in Christ Jesus" (Philippians 3:13-14). You can't make progress while you are stuck in the past.