I am not sure you want a rehearing, but it sounds like you do want to present a defense of some sort to the ticket. If you have no defense, stop reading.
Assuming you have a defense that you want to present, I would speak to the clerk in the courtroom where you were supposed to be, but were not due to the medical emergency. Show the clerk - hand her - a photocopy of the medical records from the ER that shows the condition was a medical emergency. The clerk should then talk to the judge. These things do happen, but many people are not truthful about such an excuse. Bring documentation to show the clerk (not just a filing window). Ask if the clerk will allow you to do an oral motion for "nun pro tunc" to turn back time to the date of the hearing to perhaps reset it in the future in case the officer needs to be present (again).