It is unlikely that these "arrests" while show up in your FBI Identification Record. Since I do not know the details of your "arrests," I must speak in generalities.
The information in this FBI Id Record comes from fingerprint submissions made to the FBI by the arresting agency. In all likelihood since you never appeared in Court the police never processed your arrest. If these arrests occurred in your home state, you probably would have been notified when you renewed your driver's license.
You do not mention that police even took your fingerprints. If they didn't then they could not have submitted your prints to the FBI so the FBI will not have a record.
You indicate that you plan to order your record from the FBI. Here is a link to the FBI website page for doing so: http://www.fbi.gov/hq/cjisd/fprequest.htm.
You may want to consider contacting a local attorney to check on the status of these records. Look for any attorney who appears regularly in the court which would have heard your case(s) if you had been processed. An attorney may do this for you for a small fee in anticipation that if charges are open against you, you will retain him or her to assist you to dispose of them. Your local bar association may have a lawyer referral service.