I used to fight a lot a few years ago, but I stopped when I sought the Lord. Guys have started to take advantage of me not fighting by provoking me and bullying me. Guys who are one or two years younger also push me around. While playing football they just push me around. I follow this verse from the Bible, "Vengeance is mine," but sometimes I get really angry and fight. It happened only once or twice. So my question is: Is it a sin to get angry like this?
A Christian is not to start fights, but it doesn't mean he cannot defend himself. See: Self-Defense and The Use of Force.
There are times when anger might be appropriate, but for the most part anger is something a Christian tries to avoid because it is hard to make good decisions when you are angry. "So then, my beloved brethren, let every man be swift to hear, slow to speak, slow to wrath; for the wrath of man does not produce the righteousness of God" (James 1:19-20). Notice that James said we are to be slow to anger, not never angry. It should take quite a bit to cause a Christian to become angry. See: Anger.
The problem you are having is that you are letting other people annoy you until you reach the breaking point and then you lose control. This is the wrong kind of anger to get involved in. What you need to work on is convincing people not to pick on you. One of the best ways is to become friendly with people. "Repay no one evil for evil. Have regard for good things in the sight of all men. If it is possible, as much as depends on you, live peaceably with all men. Beloved, do not avenge yourselves, but rather give place to wrath; for it is written, "Vengeance is Mine, I will repay," says the Lord. Therefore "If your enemy is hungry, feed him; If he is thirsty, give him a drink; For in so doing you will heap coals of fire on his head." Do not be overcome by evil, but overcome evil with good" (Romans 12:17-21).