Ohio and South Carolina are both part of the Driver License Compact so the speeding ticket from SC will be transferred from the South Carolina DMV to the Ohio Bureau of Motor Vehicles at which time it will likely be put on your Ohio driving record.

If points are assigned to your Ohio record for out of state offenses the state might only assess the points that the violation would have been charged if it happened in Ohio. If that is the case then going 10 mph over the speed limit in a 55 mph zone is 0 points according to the new Ohio points system. It has been reported that Ohio does not assess points for out of state minor traffic violations but you would need to check with the BMV to be certain.

If points are assigned to your Ohio motor vehicle record (MVR), you can check with the BMV to see if taking a defensive driving course or other types of traffic school will help to remove points.