C172 PLT HAS A RWY EXCURSION.

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I HAD AN 'INCIDENT.' WHILE LNDG; AFTER TOUCHING DOWN THE ACFT VEERED HARD TO THE R. I ATTEMPTED HARD L RUDDER BUT THE ACFT BEGAN TO SKID SIDEWAYS; AND ALMOST ROLLED OVER. SO I TRIED TO HOLD IT STRAIGHT WHILE I APPLIED FULL BRAKES. THE ACFT SKIDDED TO A HALT AND CAME TO REST OFF THE RWY IN THE GRASS. I WAS NOT INJURED AND THERE WAS NO DAMAGE TO THE ACFT. THE TWR ASKED FOR ASSISTANCE; I SAID I WAS FINE BUT THE FIRE DEPT CAME OUT ANYWAY AS A PRECAUTION. JUST SOME RATTLED NERVES. THE ACFT IS A C172P; THE RWY WAS RWY 14 AND THE WINDS WERE CALM. I SPOKE TO MY INSTRUCTOR TODAY. SHE TOLD ME THE MAINT DEPT EXAMINED THE PLANE. THEY REPLACED THE FRONT TIRE; IT HAD NO TREAD LEFT. BUT SHE SAID THEY FOUND NOTHING WRONG WITH THE STEERING/RUDDER SYS. BUT SHE ALSO TOLD ME THAT THEY ARE STILL EXAMINING IT AND HAVE NOT RELEASED IT BACK TO THE STUDENTS. I DON'T THINK I TEMPORARILY FORGOT MY R FROM L WHEN I LANDED. AND I FEEL I DIDN'T OVER CORRECT THE CTL INPUTS. AT LEAST HALF OF MY TOTAL FLT TIME HAS BEEN ACQUIRED IN THE VERY SAME ACFT.