What state are you in? These laws can be state specific.
In general, convictions do NOT automatically drop off your record when you transition from a minor to an adult. Usually, there is a process you must go through to get the court to sign off on it, and you generally must already be off of probation and have fulfilled your sentence.
Not all offenses will be permitted to be sealed or expunged, it all depends on the offense and the laws of your unnamed state.