DELAYED CLRNC FOR A VISUAL APCH CREATED A RWY OVERSHOOT FOR A DC9 HAVING SIMILAR CALL SIGN PROBS AND FREQ CONGESTION AT DTW; MI.

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ON APCH INTO DETROIT; WE WERE BEING VECTORED BEHIND FLT XYZ. OUR CALLSIGN WAS AXYZ; WHICH MADE THE CONSEQUENT EVENTS MORE CONFUSING. WE DSNDED TO 4000 FT MSL AND WERE ASSIGNED A HDG OF 140 DEGS BY ATC. WE PICKED UP THE FIELD AT ABOUT 15 MI AND FLT XYZ; WHO WAS IMMEDIATELY AHEAD OF US; WAS CLRED VISUAL TO RWY 22R. WE CALLED THE ARPT IN SIGHT AND THE CTLR RESPONDED 'ROGER.' MEANWHILE; THE SAME CTLR WAS VECTORING A MEDICAL EMER TO RWY 22L. HE WAS COMMUNICATING TO FLT XYZ THE EMER'S LOCATION SINCE THE 2 RWYS ARE CLOSE TOGETHER. AS EVENTS UNFOLDED; WE SAW THAT WE WERE GOING TO CROSS THE CTRLINE OF RWY 22R SENDING US TOWARD THE APCH CORRIDOR FOR RWY 21L. WE CALLED REPEATEDLY TO ATC TO GET CLRNC TO TURN TO RWY 22R; BUT WERE REPEATEDLY BLOCKED BY COM BTWN ATC; FLT XYZ; AND THE MEDICAL EMER. WHEN WE FINALLY GOT THROUGH; THE CTLR ASKED US WHY WE HADN'T TURNED FOR THE VISUAL TO RWY 22R. WE RESPONDED THAT WE HAD NEVER BEEN CLRED FOR THE VISUAL. FORTUNATELY; NO ONE WAS ON APCH TO RWY 21L; SO THE CTLR CLRED US TO TURN TO AND LAND ON RWY 21L. WE ENDED UP XING THE APCH CORRIDOR FOR RWY 22R AND RWY 21L! I SPOKE PERSONALLY WITH THE ATC SUPVR AND HE SAID THAT THE CTLR COULD NOT REMEMBER IF HE CLRED US FOR THE VISUAL OR NOT (HE DID NOT). I BELIEVE THIS INCIDENT WAS CAUSED BY SIMILAR CALL SIGNS (XYZ AND AXYZ) AND THE HIGH WORKLOAD ON THE CTLR BY SEPARATING THE MEDICAL ACFT WITH FLT XYZ.