I believe the third option on AMCAS applies to situations like deferred adjudication (i.e. guilty plea but no entry of conviction by court, do community service / take a class or whatever, then after a set period of time, the court dismisses the charge and you can legally claim you have never been convicted of a crime).
I do think it's worth finding out whether or not your charge has actually been dismissed or if it's considered a conviction. You don't want to list it if you're not legally obligated to. Also, keep in mind you're going to have to do this over and over again (residency apps, licensing, etc.) so it's better to get a clear understanding now of whether you have a conviction or if your charge was actually dismissed.
That being said, it's not going to kill your app if you have to list it. Underage drinking is pretty much the most innocuous misdemeanor out there. But again, don't list if you don't have to.