If you're looking for the state highway department, that's SCDOT (Department of Transportation). They use a collection of non-networked analog VHF-Low repeaters throughout the state. A list of those repeaters, including one in Conway, is available here:
Scanner Frequencies and Radio Frequency Reference for SC Department of Transportation (SC DOT) (South Carolina)
www.radioreference.com
If you're looking for the County agency that maintains county roads and bridges, then you're looking for Horry County Public Works.
Public Works - Horry County SC.Gov
It would seem most likely that they would use the Horry County trunked radio system here:
Horry County Trunking System, Myrtle Beach, South Carolina
We don't have any talkgroups identified on this system being used by any county agencies that are not public safety agencies. Perhaps county agencies use a different radio system that hasn't yet been documented, or they don't use a radio system that can be monitored. Perhaps they use some time of commercial wireless/cellular network.