PLT ON INST PROFICIENCY CHK IS UNDER THE HOOD AND IS GIVEN VFR TFC AFTER MISSED APCH. TFC IS NOT SIGHTED AND AFTER THE THIRD ADVISORY BY ATC; PLT REQUESTS 4000 FT ALT. ATC SAYS NO; MAINTAIN 3000 FT. A BIT OF CONTROVERSY DEVELOPS BTWN CTLR AND PLT. TFC IS NEVER SIGHTED.

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I WAS FLYING THE PUBLISHED MISSED APCH PROC FOR THE ILS RWY 28 AT ALLEGHENY COUNTY ON AN INST FLT PLAN. I WAS UNDER THE HOOD. THE INST INSTRUCTOR IN THE R SEAT WAS PERFORMING AN INST PROFICIENCY CHK. SHORTLY AFTER I RPTED THE MISS; THE CTLR RPTED 'VFR TFC; 3000 FT; OVER THE VOR.' THE INSTRUCTOR LOOKED FOR TFC AS I CONTINUED MY CLB TO 3000 FT; ENRTE TO THE VOR. WE RPTED 'NO JOY.' THE CTLR REPEATED THE TFC RPT; ADDING; '12 O'CLOCK; 1 MI.' WE AGAIN RPTED WE DID NOT HAVE THE TFC IN SIGHT. AT THE CTLR'S THIRD RPT ON THE SAME TFC; I BEGAN TO CLB (MAX 3500); WHILE RPTING THE TFC NOT IN SIGHT AND REQUESTING 4000 FT TO AVOID TFC. THE CTLR RESPONDED WITH 'MAINTAIN 3000 FT; DO YOU WANT TO CANCEL IFR?' I RESPONDED I DID NOT WANT TO CANCEL; BUT ALSO DID NOT WANT TO COLLIDE WITH VFR TFC. SHE ASKED; 'STATE INTENTIONS.' I REQUESTED TO BREAK OFF THE ATTEMPTED HOLD FOR VECTORS TO ANOTHER ILS. THE REST OF MY APCHS AND HOLDS WERE UNEVENTFUL. I FILED THIS RPT BECAUSE THE CTLR GOT SNIPPY WITH ME AND I WONDERED IF HER COLLISION ALARM WENT OFF. I'M NOT SURE WHAT ELSE I COULD HAVE DONE. WE NEVER DID SEE THE TFC.