We need to start by simply admitting it. There is no Biblical reason to have a sense of guilt over simply feeling anger. The sin is not in what we feel, but in what we do with those feelings. Anger is a very natural emotion. It is simply a part of being a human being.
Anger is as much a part of our human nature as becoming tired or getting hungry.
Anger in and of itself isn't necessarily a bad thing. What's bad is what we do with our anger. In fact, there are times when anger can be the most appropriate response to a situation. The Bible indicates on more than one occasion that God became angry. But Gods anger is just, slow in coming, and usually tempered by a chance for one to be forgiven.