FLC OF AN MLG FAILED TO TURN AFTER TKOF AS INSTRUCTED BY ATC RESULTING IN ATC INTERVENTION.

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ON MAR/MON/95; BTWN XX30 AND XX45 HRS; WE DEPARTED CHS OFF RWY 33 (9001 FT). WE WERE ASSIGNED A HDG BY TWR AFTER DEP; A R TURN TO A HDG; I DON'T RECALL. I BARELY REMEMBER READING IT BACK TO THE TWR. AFTER LIFTOFF; THE CAPT (NFP AT THE TIME); REACHED UP AND CTRED THE HDG BUG. I THEN ASKED HIM WHAT HDG WE WERE ASSIGNED. AT THAT TIME; TWR TOLD US TO CONTACT DEP. DURING THE CALL FROM TWR; I WAS LISTENING FOR THE PREVIOUSLY ASSIGNED HDG BY THE TWR; FROM THE TWR CTLR; THINKING THE CTLR WOULD AGAIN ASSIGN OR REMIND US OF HDG. THERE WAS NOT ANOTHER ASSIGNMENT OR REMINDER. BY THIS TIME THE CAPT AND MYSELF NOTICED TFC APCHING TO LAND ON OPPOSITE END OF OUR DEPT RWY. THERE WAS NEVER AT ANY TIME A CONFLICT. AT ONCE THE CAPT TURNED THE ACFT TO THE L TO AVOID ANY KIND OF CONFLICT AND THEN THE APCH CTLR GAVE US AN IMMEDIATE R TURN; EVIDENTLY NOT NOTICING THAT WE HAD ALREADY TURNED AWAY FROM THE APCHING ACFT. AT THIS TIME WE WERE AT 2000 FT AND THE OTHER ACFT WAS RPTED DSNDING OUT OF 1700 FT APPROX 5 MI OUT. WE TURNED AS DIRECTED BY DEP AND APOLOGIZED FOR THE CONFUSION AND REASSURED DEP CTL WE HAD THE OTHER ACFT IN VIEW AND THAT THERE WAS NO CONFLICT. WE ALSO CONTACTED TWR AND APOLOGIZED FOR THE CONFUSION LATER. I PERSONALLY HAVE ADOPTED A MORE DISCIPLINED RESPONSE AND AWARENESS TO TWR INSTRUCTIONS FOR TKOF AND DEP PROCS.