SWIM had a similar situation come up. He was told explicitly by his attorney to never bring any of this up to anyone, as no medical boards would look at a juvenile record and it would only cause discrimination. The only difference what that he was a minor (under 18.)
When I was applying to schools this became something of an interest to me. I looked into what the AMA had to say about it, and their claim was that they were worried about only a few key offenses, namely previous drug charges, assault of someone under your care, especially sexual, and violent convictions. During our first month of class, they made us all get background checks. This created a lot of worry among students who had previous minor offenses and DUIs. Eventually, the head of the department came and told us that they were only looking back five or six years, only at adult records, and that any minor offenses would have to be explained in an essay. I never heard of anyone having an issue with it.
I would speak to an attorney about the ability of state medical boards to look at your record, but I doubt that a medical school will find it if it was only an arrest. Also, without a conviction you will probably have little trouble gaining a license (courtesy of my friends in law school living next door
)