The real problem you may have is that you were likely adjudicated guilty if you only paid a fine back in 1986. As teh law required probation if the court were to withhold adjudication. And you would be ineligible to ever get your record sealed or expunged if you were adjudicated guilty.
You should consult with an attorney for information on sealing the records related to your case. If you are eligible, and the court seals your record, you can legally state on an application that you have never been arrested or charged with a crime. Our firm offers free consultations for matters relating to criminal charges, so please feel free to contact us.