GA C172 PLT DEPARTS AND COMES INTO CONFLICT WITH AN ATR ON FINAL APCH WHILE CONDUCTING A VFR SCENIC FLT.

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I (ACFT X) WAS DEPARTING FROM EYW IN A C172. I WAS SITTING IN THE R SEAT. I REQUESTED TO TWR; WHILE I WAS TAXIING FROM THE TAMP; TO TAXI TO RWY 9; AND IF I COULD TAKE A SCENIC FLT OF THE ISLAND AT 1000 FT. TWR CTLR GAVE ME A R TURN AFTER TKOF TO HDG 270 DEGS AND TOLD TO RPT WHEN I WAS GOING TO TURN TO THE N. HE POINTED OUT TFC (HELI BELL 206; ACFT Z) OPERATING OVER A CRUISE SHIP AT 500 FT BELOW; AND ANOTHER ACFT Y APCHING THE ARPT IN THE OPPOSITE DIRECTION THAN MINE. THAT DAY THERE WAS A GOOD XWIND FROM THE S. SO AFTER I DEPARTED AND TURNED TO HDG 270 DEGS; I NOTICED THAT I WAS CONTINUOUSLY CORRECTING MY HDG TO THE L TO STAY ON THE SHORELINE. THE TWR (ATC) WAS VERY BUSY AND I DIDN'T HAVE TOO MUCH TIME TO SPEAK TO HIM. I WAS TRYING TO TURN TO THE N; BUT PLANES KEPT COMING INTO THE FREQ; ASKING AND OVERLOADING THE ATC FREQ. SO I CONTINUED MY FLT TO HDG 270 DEGS. AT THAT POINT; THE ISLAND WAS ON MY TAIL AND I DIDN'T HAVE ANY VISUAL REF FOR MY GND PATH. I THINK THE WIND DRIFTED ME CLOSE TO THE FINAL APCH FOR RWY 9; WHILE A BIG TURBOPROP (PROBABLY AN ATR Y MODEL) WAS ON FINAL APCH; DSNDING FROM A HIGHER ALT. HE NOTIFIED THE TWR OF MY PRESENCE AND HE DECLARED THE MISSED APCH. I SAW THE AIRPLANE WHEN HE WAS ABOUT 300-400 FT OVER ME; ALMOST IN MY BACK (TAIL) ABOUT 1/2 - 1 MI DISTANCE. I TALKED WITH THE TWR AND ASKED THEM TO ALLOW ME TO OVERFLY; AT 1000 FT; THE COAST GUARD STATION. THAT IS ABOUT 30-40 DEGS OFF THE EXTENDED CTRLINE FROM RWY 9. HE CLRED ME AND INSTRUCTED ME TO ADVISE HIM WHEN I WAS IN THE VICINITY. I TRIED 2 OR 3 TIMES; BUT HE NEVER ANSWERED ME. I COULD HEAR THAT THE AIRSPACE WAS GETTING SATURATED. HE CLRED SOME OTHER ACFT TO LAND. AT THAT MOMENT; I WAS OVER THE COAST GUARD STATION. I WAS TURNING NBOUND IN A L TURN WHILE I HEARD ANOTHER ACFT SAYING THAT HE HAD A C172 IN FRONT OF HIM AND HE COULDN'T LAND. I THOUGHT THAT THAT AIRPLANE WAS TALKING ABOUT ME. IN FACT; I SAW THE AIRPLANE ON MY L WHERE I FINISHED MY L TURN. THE TWR QUESTIONED WHO WAS THE MENTIONED ACFT ON FINAL FOR RWY 9? I ANSWERED WITH MY N-NUMBER AND MY POS AND ALT. THEN THE TWR ASKED ME TO PROCEED NBOUND TO MY DEST BECAUSE I WAS GETTING BUSY. I TOLD THEM THAT I TRIED TO CALL AND I PROCEEDED IN MY FLT.