PA28-181 PLT MAKES SPACING TURN IN THE TFC PATTERN WITHOUT THE PROPER CLRNC.

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I WAS ON R DOWNWIND FOR RWY 31; AND WAS CLRED TO LAND; #2 BEHIND A PIPER NAVAJO. THE NAVAJO EXTENDED HIS DOWNWIND AND I ALSO EXTENDED MY DOWNWIND SINCE I WAS TOLD TO FOLLOW HIM. BEHIND ME WAS A PIPER ARROW. THE CTLR TOLD THE ARROW THAT HE WAS #4 (THOUGH HE WAS REALLY #3); AND CLRED HIM TO LAND. WHEN THE NAVAJO WAS ON FINAL TO RWY 31; I STARTED A TURN TO R BASE. THE ARROW WAS BEHIND ME AND REQUESTED TO TURN BASE SO THAT HE COULD LAND IN FRONT OF ME. I ASKED THE ARROW WHERE HE WAS; AND HE RESPONDED THAT HE WAS INSIDE OF ME. THE CTLR SAID 'ARROW; YOU ARE RUNNING THE SHOW.' I DID NOT HAVE THE ARROW IN SIGHT AND WAS CONCERNED ABOUT A POSSIBLE COLLISION ON FINAL; SO INSTEAD OF MAKING A R TURN TO FINAL; I DECIDED TO CIRCLE TO THE L. THE CTLR WAS MAD AND ASKED ME WHAT I WAS DOING. THE CTLR VECTORED ME BACK TO A LONG FINAL; AND CLRED FOR TKOF A DC9 THAT HAD BEEN HOLDING SHORT OF THE RWY. I THEN LANDED WITH NO FURTHER PROBS. TO AVOID THIS INCIDENT; I SHOULD HAVE ASKED THE CTLR WHERE THE ARROW WAS; AND REQUESTED VERIFICATION THAT THERE WAS NO CONFLICT. I ALSO SHOULD HAVE IMMEDIATELY INFORMED THE CTLR WHEN I TURNED AWAY FROM THE RWY. FOR HIS PART; THE CTLR SHOULD HAVE USED STANDARD PHRASEOLOGY; AND SHOULD HAVE CLARIFIED THAT I WAS NOW TO FOLLOW THE ARROW.