Background check for a job?

i got in trouble a few years back (over 3 years ago, i was 19) for pot and got 2 cl b misdemeanors and went to court when i talked to the prosecutor he told me i would get a continence with out a finding for one year and i had to do 25 hours of community service and not got get in trouble i would be all set...will this show up in a background check for a hospital job...(that was my rock bottom and haven't done anything bad since then) i also have a friend who is a cop who did a check with his computer and all he could find is my car accident i had in 2005. i'm i good?