In the American culture, it’s nearly impossible to avoid violence. Violence can be found in television shows, movies, books, and thus it is unavoidable. In your case, however, your thoughts of violence and killing are coupled with anger. You experienced a wave of anger which triggered thoughts of killing. It is not a healthy response to anger.
No one has the right to harm another person, even when they are angry. Anger does not justify violence. Some people might respond to anger with violence but it in no way justifies their behavior. It is good that you have never harmed anyone. It’s important to ensure that it never happens.
My recommendation is to enter counseling to learn to deal with your anger. It’s concerning that you thought of killing in response to anger. Thinking of killing and the act of killing are indeed very different but your thoughts might indicate that your anger is growing. You’ve tried breathing exercises but they did not work. You should consult a mental health professional who specializes in anger management. There are many approaches to treating anger including group therapy, psychotherapy and medication. Please take care.