Kentucky and Ohio are both part of the Drivers License Compact so Ohio will report your ticket to Kentucky and thus it will likely show up on your KY driving record. Kentucky though does not assess points for out of state speeding tickets, though it will for other types of tickets.

Kentucky's traffic school can be referred to by the court system and since your ticket was in OH and not KY then it is doubtful that you could do traffic school. The speeding ticket in Ohio could affect your insurance rates in Kentucky when it shows up on your record.

Insurance companies differ on their rating system though and how speeding tickets affect your premiums. So if you do not want to just pay the ticket and have it show up on your driving record you could contact an Ohio lawyer to see what options you have.

Ohio auto insurance rates can be found here.