If I was arrested and charged as a 15 year old juvenile, went in front of a judge and was instructed to report to a probation officer and counseling for a period of time while my case was under review, but then my case was formally dismissed by the same judge, is that defined as a conviction?
You appear to be writing this question from Rhode Island so, here is a general answer for that state. Generally speaking, successful completion of probation will not lead to a criminal conviction in Rhode Island, unless it was accompanied by a suspended sentence and/or a fine. In your case, the ultimate disposition was a dismissal, so you should not have a juvenile record. If you had a lawyer representing you for that case, you should call that lawyer for more specifics and to determine whether that case resulted in a criminal record.