Just my own anecdotal story....
I was arrested for DUI a few years ago. Obviously, I wrote an addendum.
I did not seek treatment or otherwise attend counseling. However, since it is the only blemish on my record, I was told by the few law schools I asked that it would not adversely affect the bar and it obviously has not affected my admissions. They want to see if there is a pattern of behavior. I have a "blip." (Albeit, a DUI is a very serious thing
) You have what may be considered a pattern.
I would think it couldn't hurt to get into some type of alcohol course that gives you a certificate. This will show you addressed the behavior issue. I can argue I suffered a lapse, an anomaly of character...which is true, as I barely even consume. But when these actions take place more than once it becomes a behavior pattern. Think of it as two dots on a chart. You can draw a line from them, make connections in a chronology. If you address it properly, you still should be able to get into law school. I would call the bars for the states you are interested in and ask them what you can do to make yourself a better candidate, too. But first of all, you need to stop putting yourself in the situations or stop drinking. And DO NOT get into trouble while in law school.