PIPER CPR PLT OPERATES ACFT AFTER GEAR UP LNDG DAMAGES THE WING FLAPS AND PROPS.

Narrative

I FLEW FROM F45 (NORTH PALM BEACH COUNTY) TO TREASURE CAY; BAHAMAS (MYAT). I FAILED TO EXTEND THE LNDG GEAR AND CONTACTED THE RWY WITH THE INBOARD TRAILING EDGE OF THE FLAPS AND THE PROP TIPS. I WENT AROUND AND LANDED NORMALLY. UPON INSPECTING THE ACFT; I FOUND THE FLAPS WERE ABRADED BUT FUNCTIONAL. THE 4-BLADE 'Q-TIP' PROPS WERE CURLED AND SOMEWHAT ABRADED BUT SEEMED STRUCTURALLY SOUND. I DID A FULL PWR RUN-UP; THEN TEST FLEW THE ACFT. IT BEHAVED NORMALLY; AND I FELT THAT IT WAS OK TO FLY IT. I CONTINUED TO NASSAU; PICKED UP THE OWNER OF THE ACFT; AND SAID NOTHING OF WHAT HAPPENED. WE CONTINUED TO PBI AND ON TO F45. I DROPPED HIM OFF AND RETURNED TO BASE (BCT). THE ISSUE HERE IS MY DECISION TO CONTINUE FLYING THE ACFT AFTER IT WAS DAMAGED. I AM NOT AN A&P; NOR WAS I AWARE AT THE TIME THE SERIOUSNESS OF ANY PROP CONTACT. I THOUGHT THAT SUDDEN STOPPAGE WAS THE ONLY DANGER TO THE ENGS; AND AS I STATED; THE PROPS SEEMED OK. CONTRIBUTING FACTORS INCLUDE A HIGHLY EMOTIONAL STATE; CLOSE TO SHOCK. ALSO; I HAD ONLY FLOWN 25 HRS IN THE PAST 90 DAYS; AND HAD ONLY 4 HRS IN TYPE. IF I WERE IN A SIMILAR SIT TODAY; I WOULD NOT HAVE FLOWN THE AIRPLANE HOME; BECAUSE I AM MORE AWARE OF THE POTENTIAL FOR CATASTROPHIC FAILURE OF THE ENGS AND PROPS FOLLOWING AN EVENT SUCH AS THIS.