A coworker asked for my forgiveness, but because the moment was awkward, I didn’t say “I forgive you.” There’s a good chance that I have a form of OCD, and I get stuck on little things like this. I went out of my way to be nice to him, and I never mentioned what happened to anybody. Now I’m caught up in the fact that I didn’t really rebuke him or encourage him to be more godly after the fact. I feel like I didn’t do enough, and I know we’re not supposed to go by feelings, but it still bothers me.
You seem to be trying to turn the teachings of Christ into a set of rituals to be done, instead of understanding what is being required of you.
When there is a disagreement between two people, the goal is to settle the matter as quickly as possible. Matters left unresolved have a strong tendency to blow up and get worse. "Make friends quickly with your opponent at law while you are with him on the way, so that your opponent may not hand you over to the judge, and the judge to the officer, and you be thrown into prison. Truly I say to you, you will not come out of there until you have paid up the last cent" (Matthew 5:25-26).
Unfortunately, the person who did you wrong either is unaware he did something wrong, didn't think it mattered or doesn't care. The reason you need to bring up the problem and explain why it was wrong is to hopefully change his mind about the matter. When he does change, then you can offer him forgiveness so that the matter is resolved. "If your brother sins, rebuke him; and if he repents, forgive him" (Luke 17:3).
In your case, the person realized he was wrong before you brought up the matter to him and he apologized. You forgave him and, thus, the conflict is now ended. There was no need for a rebuke because he already changed.