C172 INSTRUCTOR AND STUDENT HAD A CONFLICT WITH ANOTHER C172 IN THE PATTERN AT COS.

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MY STUDENT AND I HAD COME IN FOR A TOUCH AND GO ON RWY 17R AND PROCEEDED ON UPWIND. WE HAD NOT RECEIVED ANY INSTRUCTIONS ON WHICH TFC TO MAKE; SO I ASKED AND WAS TOLD TO MAKE R TFC. WHILE ON DOWNWIND ABEAM THE NUMBERS; I SAW 2 ACFT ON FINAL AND HEARD A THIRD ON THE OPPOSITE DOWNWIND. I WAS NOT INSTRUCTED TO EXTEND DOWNWIND SO I PROCEEDED ON TO BASE AT THE APPROPRIATE TIME. I FOUND OUT THAT WE HAD PROCEEDED IN FRONT OF ANOTHER ACFT WHEN SHE CALLED ME IN SIGHT AND ASKED IF SHE WAS SUPPOSED TO FOLLOW ME. I BELIEVE THAT THERE WERE A FEW CONTRIBUTING FACTORS IN THIS INCIDENT. ONE WAS THAT THERE WERE A LOT OF ACFT IN THE PATTERN WITH SIMILAR CALL SIGNS. ANOTHER WAS THAT THE CTLR WAS NOT CLR ABOUT WHICH ACFT OR HOW MANY WE WERE SUPPOSED TO GIVE WAY TO. THE CTLR SOUNDED STRESSED EVEN BEFORE THIS AND HAD BEEN SNIPPY WITH SOME OF THE ACFT; THIS COULD HAVE AFFECTED HIS ABILITY TO CONCENTRATE ON PROVIDING ADEQUATE SEPARATION. AS PIC; I SHOULD HAVE CONTINUED ON DOWNWIND UNTIL I WAS CLRED TO TURN; OR AT LEAST UNTIL HE SAID SOMETHING TO ME. I THINK THAT HE SHOULD HAVE MADE IT CLR TO EACH ACFT WHICH ONE THEY WERE FOLLOWING. THERE WAS NO COM BTWN THE CTL TWR AND MY ACFT FROM UPWIND WHEN I INITIATED IT ALL THE WAY UNTIL FINAL.