People's feelings change, especially when it comes to affairs of the heart, and even more particularly when one is young. You state that your brother's behavior is out of character. I assume that refers to the drinking, self-mutilation, and fighting. The magnitude and duration of your brother's reaction to the break-up leads me to wonder whether this event triggered a deeper, underlying issue that needs professional attention. Self-mutilation is dangerous.
People can do serious damage to themselves, especially when under the influence of alcohol.
I wonder whether this incident might have touched off some feelings of low self-esteem, powerlessness, or underlying depression. You might encourage him to seek out a consultation with a professional psychologist. It is unfortunate that people have a bias against seeking a professional for their mental health concerns, while even professional athletes will seek a professional consultation for their physical health concerns. Just as one can wait too long to seek medical help, one can wait too long to seek psychological help. The issue of trying to help someone help themselves, as you put it, is difficult.