First Offense in South Carolina-Speeding 71/60 and warning for no regist....HELP!!!?

I want to fight my speeding ticket because I was never speeding. I was on a 4 lane highway divided by a gr. The state trooper that issued me the speeding ticket was on the left lane(slow lane on the left of the road) with a car in the fast lane, while I was on the right in the farthest lane with a car beside me and a car that went around me going faster while I was doing 57/60. When the officer stopped me I let him know that I was traveling to get my speedometer checked b/c it wasn't working properly i could go no faster than 60 miles....so how was I speeding...I have clean driving criminial and credit report. I'm an 19 yr old female dean list student and I took defensive driving course. How should I fight this ticket? Do I need a laywer? Do I need a jury trial or can I get it dropped by showing my mechanic's letter to the judge one on one that states b/c my speedometer wasn't working properly I wasn't able to exceed more than 60 miles? I NEED HELP! PLZ