There is an idea that anger, in itself, is a sin. That Christians should always be truly content in all things, peaceful, happy, never let that smile fall. But anger is not the sin, for the Lord Himself feels it. In truth, there are many things about which we should be angry.
There are obviously times in which anger is not acceptable. The example that springs immediately to mind is a story I once heard about a young man who was given a car as a gift, which he promptly destroyed because he hated it. But should we not be angry when people behave rudely? Should we not be angry when people are selfish? Should we not be angry when people are reckless? What about when people are cruel, unjust, even violent? When people lie, when people cheat, when people oppress, these are all good reasons to be angry. And so the scriptures do not tell us to avoid anger, but to be temporarily angry, and not to sin in anger.
Once we have determined the difference between wicked and righteous anger, the question is what do we do with it? If it is wicked anger, the obvious answer is to crucify it. But righteous anger demands an adequate, non-sinful response. Do two wrongs make a right? Not at all. Such anger only opens the door for more evil to take place, only this time you're the one doing it. But sin dies when the one who is justly angry places it in the hand of the one who judges justly.
The Gospel begins with God's own righteous anger against us. When we sin, God is justly angry. It is against His Holy nature to allow evil to stand. And yet, rather than letting the sun go down on His anger, He sent His Son down to absorb it. Every sin we have ever committed, or will ever commit, died on the cross, and it did not rise with Jesus. Instead, we will.
As Christians, we are called to imitate Christ (1 Corinthians 11:1). If we are to be conformed to His image, we must avoid sin, but give as much space as possible to mercy, grace and love. When someone makes us angry, there is no shame in seeking to correct them. There are good, Godly ways to do this. But as John Macarthur says, "you are never more like Christ than when you forgive."
Perhaps the person who made you angry will never repent of it. Whether they are oblivious, or consciously aware and yet apathetic, perhaps they will remain in their sin against you. This is especially likely with unbelievers, though our fellow Christians are not always loving either. But even in this case, you gain nothing from your own fury.
I speak from experience. I gained nothing from my wrath, but I failed to receive many great blessings, and worse, I tarnished the image of my God. Of course, I still love the Lord, and am called according to His purpose, and so even this worked out for the good (Romans 8:28). But I pray that some of that good will be that I can encourage at least one reader in a difficult time in their own lives, let that anger go, lest the devil Himself should sit on your shoulder. Give no place to him, but only to the Holy Spirit, whose fruits are love, joy, peace, longsuffering, kindness, goodness, faithfulness, gentleness and self-control (Galatians 5:22-23).