STUDENT PLT ABOARD C172 HAS RWY EXCURSION AFTER LNDG. FLAT RIGHT MAIN GEAR TIRE MAY HAVE CONTRIBUTED.

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I WAS APCHING RWY XX FOR A FULL STOP LNDG TO FINISH MY SOLO XCOUNTRY FROM ZZZ TO ZZZ1; A REQUIRED STEP TOWARDS OBTAINING MY PVT PLT'S LICENSE. AT ZZZ1; I HAD A DECENT LNDG. THE AIRPLANE HANDLED FINE; AND I TAXIED BACK TO THE RWY AND TOOK OF AGAIN TO HEAD DIRECT TO ZZZ. I ENTERED A R BASE FOR RWY XX AT ZZZ AFTER RPTING 3 MI OUT FROM THE FIELD. I HAD ALREADY OBTAINED THE ATIS AND CHKED MY FUEL SELECTOR VALVE; FUEL SHUTOFF; ADJUSTED THE TRIM SLIGHTLY; MADE SURE THE MIXTURE WAS RICH; AND DID A BRIEF SCAN OF MY INSTS. I ALSO TURNED ON MY LNDG AND TAXI LIGHTS (BEACON AND STROBE WERE ALREADY ON). AS I TURNED FINAL; I LOOKED AT THE WINDSOCK AND IT APPEARED TO BE ALMOST ALIGNED WITH THE RWY; BUT WITH A SLIGHT L XWIND. AS I WAS DSNDING; THE AIRPLANE FELT LIKE I NEEDED TO KEEP IN A LOT OF R RUDDER IN ORDER TO KEEP IT ALIGNED WITH THE RWY. I APPLIED XWIND CORRECTION WITH THE AILERONS AND HAD A SLIGHTLY HIGH APCH (THE PAPI'S INITIALLY WERE 3 WHITE AND 1 RED; BUT I WAS ABLE TO CORRECT FOR GS AND FOR THE MAJORITY OF THE APCH HAD 2 WHITE AND 2 RED LIGHTS). MY SPD WAS 75 KTS. AS I PASSED OVER THE NUMBERS; I PULLED THE PWR BACK TO IDLE. I GOT INTO GND EFFECT AND FLOATED ABOUT 50-200 FT PAST THE NUMBERS. THE TOUCHDOWN WAS GOOD (I NEEDED TO APPLY A LITTLE PWR TO KEEP IT FROM TOUCHING DOWN HARD); BUT WITHIN 2 SECONDS OF TOUCHING DOWN; THE AIRPLANE IMMEDIATELY BEGAN TO TURN TO THE R AND HEAD TOWARD THE SIDE OF THE RWY. I FELT LIKE I WAS GOING TOO FAST; BUT THIS COULD HAVE BEEN BECAUSE I WAS LOOKING MORE OUT OF THE SIDE OF THE AIRPLANE TO SEE IF I WAS GOING TO GO OFF THE RWY; SO I PULLED THE ELEVATOR FULL BACK; RELEASING MY XWIND CORRECTION AT THIS TIME. THIS DID NOT SEEM TO BE SLOWING ME DOWN; SO I APPLIED SOME L BRAKE AND ALMOST IMMEDIATELY AFTER APPLYING L BRAKE; I ALSO APPLIED FULL L RUDDER. (THE L BRAKE SEEMED UNRESPONSIVE.) I STILL WAS HEADING OFF TO THE R SIDE OF THE RWY. I THEN NEUTRALIZED THE RUDDER AND APPLIED HVY BRAKING WITH BOTH BRAKES. I THEN SLID OFF THE RWY ABOUT 10 FT PAST TXWY H. TWR ASKED IF I COULD MAKE TXWY H (I DO NOT THINK HE SAW ME RUN OFF THE RWY) AND I TOLD HIM THAT I PASSED THE TXWY AND WAS IN THE GRASS BTWN THE RWY AND TXWY. HE ASKED IF I COULD TAXI BACK TO THE RAMP. I ATTEMPTED TO DO SO; BUT THE AIRPLANE WOULD NOT MOVE. TWR TOLD ME TO POWER DOWN; WHICH I DID; AND ARPT OPS ARRIVED WITHIN ABOUT 5 MINS. THEY TOLD ME THAT THERE WAS NOTHING I COULD DO; AFTER LOOKING AT THE WEAR ON THE TIRES. THE R TIRE WAS BLOWN WHICH CAUSED ME TO VEER TO THE R.