C172 PLT HAS A CONFLICT WITH ANOTHER ACFT ON THE RWY AFTER LNDG AT PSP.

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I WAS CLRED TO LAND ON RWY 31L. IT WAS A BUSY DAY AND I PLANNED A SHORT FIELD LNDG SO AS TO EXIT THE CLOSEST HIGH SPD TXWY B EXPEDITIOUSLY TO TXWY W ON THE L SIDE. UPON LNDG I SLOWED TO MAKE THE L TURN TO EXIT BUT ENDED UP AT A 90 DEG ANGLE TO THE TXWY AT ALMOST A STOP ON THE R SIDE OF THE RWY CTRLINE. IT WAS AT THAT POINT I WAS STARTLED TO SEE THE OTHER ACFT SO CLOSE TO ME OVER THE NUMBERS IN LNDG ATTITUDE WHAT LOOKED TO BE 600 FT BEHIND AND 100 FT ABOVE. IT WAS UNCLR TO ME THE TWR'S INSTRUCTIONS; CONTINUING DOWN THE RWY WOULD HAVE BLINDED BOTH ACFT TO EACH OTHER PLACING US IN A LIKELY COLLISION IF THEY CONTINUED FOR LNDG (I HEARD NO GAR AT THIS POINT); GOING FORWARD TO EXIT THE L SIDE AS ORIGINALLY PLANNED; I WOULD HAVE CROSSED THE LNDG ACFT'S FLT PATH ALSO BLINDING EACH OTHER. SO WITH WHAT I FELT WAS AN IMMEDIATE NEED FOR ACTION FOR EVERYONE'S SAFETY I CONTINUED TO TURN L 135 DEGS AND EXITED ON TXWY B TO TXWY C WHICH WAS THE FASTEST WAY OFF THE RWY. DURING THIS I THEN HEARD THE PLT OF THE LNDG ACFT SAY 'GO AROUND.'