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.
Good luck.