HDG TRACK DEV IN A NON ADHERENCE TO AN ATC CLRNC INSTRUCTION.

Narrative

DEPARTING ON RWY 18R AT CLT THE STANDARD CLRNC WAS GIVEN AS RWY HDG; 250 KTS TILL ADVISED AND CLB TO 8000 FT EXPECT VECTORS TO ASSIGNED RTE. SHORTLY AFTER TKOF AND HAVING BEEN SWITCHED TO DEP CTL; WE WERE ASKED IF WE HAD THE TFC; A TWIN CPR JET; THAT JUST DEPARTED THE PARALLEL RWY 18L. WE RESPONDED THAT WE DID NOT HAVE THE TFC. I (THE FO) WAS FLYING THE ACFT AND ELECTED TO TURN SLIGHTLY R SINCE WE DID NOT HAVE THE TFC AND HAD JUST RECEIVED A TCASII TA ON THAT TFC. (VFR CONDITIONS 15 MI VISIBILITY.) THE CTLR ASKED WHAT OUR HDG WAS AND THE CAPT RESPONDED 190 DEGS. (RWY HDG IS 181 DEGS). THE CTLR ASKED 'WHO GAVE YOU THAT HDG?' CAPT RESPONDED; 'NO ONE DID!' THE CTLR'S TONE INDICATED THAT HE WAS NOT HAPPY WITH THAT SIT AND SHORTLY THEREAFTER TURNED US TO ABOUT A 270 DEG HDG; FOLLOWED BY AN ADDITIONAL 290 DEG OR SO HDG TO JOIN A DIRECT RTE TO SPARTANBURG; SC (GSP). WE COMPLIED AND WERE EVENTUALLY SWITCHED OFF TO THE NEXT CTLR. AT NO TIME DID WE TURN INTO KNOWN TFC. AS A FACT; WE TURNED AWAY FROM KNOWN TFC (KNOWN BY A TCASII ALERT). SAFETY WAS IN MY OPINION ENHANCED AND SAFETY WAS NOT IN QUESTION. SURFACE WINDS AT THAT TIME WERE 120 DEGS AT 9 KTS. THIS MAY HAVE MADE THE 'DRIFT' SEEM GREATER. I HAVE NO SUGGESTIONS TO REMEDY THIS 'SIT.'