"And their sins and iniquities will I remember no more." (Hebrews 10:17)
You've heard the saying, I'm sure, "Confession is good for the soul." This is always true if the confession is made to God; but I would contend that if the confession benefits your soul while wounding another's, it may be more selfish and self-serving than good.
I have seen this played in personal encounters between individuals as well as in so-called, "confess your faults" services in churches. Sentences that began, "I confess to having had bad feelings toward so-and-so because..." were always a dead give away that grievances which might have sounded petty otherwise were now going to be aired in a way that gave them more importance, while at the same time, giving the confessor the aura of profound humility. I have heard everything from perceived personal slights to sexual inadequacies in a mate pointed to on occasion. Things that could and should have been taken care of privately and individually. Otherwise, it becomes little more than a confession of our feelings about someone else's failures.
Frankly, I will have to say I've seen this tendency more often in women than men, which is not to say this is a gender-based trait. It's not. But perhaps because we women are more adept at sharing our feelings, we are, for that reason, more in danger of sharing them too often. An apology should not be taken lightly, whether it is given or received; but you will be hard pressed, I think, to find a directive from God to apologize for having "bad feelings" toward another. We are told to confess our faults (James 5:16), not our feelings.
It is God who searches the heart, and there are some things that should remain between the two of you. To do otherwise may, instead of eliminating bad feelings, only create more. It may make me feel better to tell "Jane" that I always felt hard toward her because she ended up getting the husband I wanted; but now God has given me the grace to face my sin and ask for her forgiveness. But, truthfully, if you're "Jane," what kinds of feelings toward me have now been aroused?
Don't forget, God is the only one who can—or has—promised, "Their sins and iniquities will I remember no more."