ZSU CTLR EXPERIENCED OPERROR AT FL330 WHEN MISTAKING AN OVER FLIGHT WITH AN ARR AND ISSUING CLRNC TO WRONG ACFT.

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I WAS WORKING THE SECTOR 4 AND 6 RADAR POS IN THE SAN JUAN CERAP. THERE WERE WX DEVS; MAINLY IN SECTOR 6; FOR DEP ACFT OUT OF SAN JUAN AS WELL AS INBOUND TFC COMING FROM ZMA. THE BOUNDARY WITH SANTO DOMINGO CTR WAS ALSO AFFECTED BY WX DEVS; AS TFC NORMALLY ENTERING AND EXITING DOMINICAN AIRSPACE THROUGH ZSU SECTOR 8 WAS DOING SO THROUGH SECTOR 6. THE TFC BEING WORKED WAS NOT NUMEROUS; BUT WAS COMPLEX. AT ABOUT XA05 BOTH ACFT INVOLVED IN THE INCIDENT CHK IN FROM ZMA COMING IN FARTHER N THAN USUAL. THE ACFT LNDG SAN JUAN WAS AHEAD AND TO THE S OF THE OVERFLT ACFT. THE LANDER WAS AT FL350 WHILE THE OVERFLT WAS AT FL330. THINKING THE OVERFLT WAS AN ARR I ISSUED INSTRUCTIONS TO IT THAT WOULD HAVE BROUGHT IT INTO SAN JUAN THROUGH THE NORTHERN GATE OF THE APCH SECTOR; LEAVING THE WESTERN GATE FOR THE OTHER ACFT WHICH WAS S OF THAT ACFT AT THAT TIME. WHEN THE PLT QUESTIONED THE CLRNC I VERIFIED THE FLT STRIP AND REALIZED IT WAS AN OVERFLT; SO I PROCEEDED TO CLR IT TO THE COMMON POINT ALONG THE SAN JUAN AND PIARCO CTR BOUNDARIES. THAT TRACK SEEMED TO PARALLEL THE TRACK OF THE INBOUND ACFT WHICH WAS 7-8 MI S. I DECIDED TO DSND THE INBOUND ACFT FROM FL350 TO FL310 BASED ON THIS. SUDDENLY THE DECISION IS MADE TO COMBINE ALL SECTORS; WITH ME TAKING THEM ALL. THE NEXT SECTOR'S CTLR CONFIGURES MY SCOPE FROM HIS POS; CALLS AND IMMEDIATELY STARTS BRIEFING WITHOUT MY ACKNOWLEDGEMENT OF READINESS TO RECEIVE THAT SECTOR'S TFC OR AIRSPACE. WHILE BRIEFING; AN ACFT CALLS WITH A REQUEST AND ANOTHER CHKS IN FROM THE NON-RADAR SECTOR. I TELL THEM ALL TO STAND BY WHILE THE BRIEFING IS COMPLETED. AT THE SAME TIME I CONTINUE TO MONITOR THE 2 ACFT I HAVE IN CLOSE PROX. THE OTHER SECTOR ALSO HAD WX DEVS. THERE WAS ALSO AN ACFT SPEAKING TO US; BUT NOT RADAR IDENTED. AS SOON AS THE BRIEFING WAS OVER; FEELING UNEASY ABOUT THE ACFT I HAD DSNDING ALONG SIDE THE OVERFLT; I DECIDED TO TURN THE ARR AWAY FROM THE OVERFLT'S TRACK; AS THEY SEEMED TO NOW BE CONVERGING AND THE OVERFLT WAS ALSO FASTER THUS OVERTAKING THE ARR. I MISTAKENLY ISSUED A 20 DEG L TURN TO THE ARR. THIS NEW HDG PUT THE ACFT IN THE OVERFLT'S PATH. NOT REALIZING THE MISTAKE I CONTINUED TO WORK THE OTHER ACFT ON FREQ. I SWITCHED 2 ACFT FROM THE INHERITED AIRSPACE; AND THE ACFT THAT HAD A REQUEST WHILE THE POS RELIEF BRIEFING WAS TAKING PLACE ADVISED ME THAT IT STARTED TO DEVIATE. I LOOKED AT ITS FLT STRIP TO GIVE IT A CLRNC TO A POINT FURTHER AHEAD IN ITS FLT PLAN. AT THIS TIME I NOTICE THE ARR ACFT WAS EVEN CLOSER THAN I EXPECTED TO THE OVERFLT; SO I ISSUED A 10 DEG L TURN TO THE OVERFLT. I CHKED THE DISTANCE BTWN THE 2 AND FOUND THEY HAD 5.25 MI OF SEPARATION AT THE SAME ALT. I THEN SWITCHED ANOTHER ACFT TO APCH FREQ WHO THEN PROCEEDED TO TIE UP THE FREQ WITH A PERSONAL REQUEST. THIS TOOK ABOUT 30 SECONDS OF AIR TIME. BY THIS POINT I WAS UNSURE SEPARATION WAS MAINTAINED. WHEN CHKED THROUGH THE SCOPE IT SAID I HAD 4.65 MI STILL NOT CLR OF FL320. THE PLTS DID NOT ALERT ME OF ANY TCAS ALARMS NOR DID IT GET COLLISION ALERT WARNINGS. THE LOSS OF SEPARATION OCCURRED 3-4 MINS AFTER THE SECTORS WERE COMBINED. THE PROBS AROSE WITH THE POOR TIMING OF SECTOR COMBINATION WHICH TOOK AWAY FROM MY ATTN THE SEQUENCE OF THE 2 ACFT IN THE INCIDENT. THE WX DEVS REQUIRED MORE ATTN THAN USUAL; SO SECTOR COMBINATION SHOULD HAVE WAITED. WITH THE ACCEPTANCE OF AIRSPACE RESPONSIBILITY ATTN WAS TAKEN AWAY FROM AN EMINENT SITUATION AND MY MISTAKE WOULD HAVE BEEN CAUGHT ON TIME TO AVOID THE LOSS OF SEPARATION. A PLT TYING UP THE FREQ FOR PERSONAL REASONS ALSO ADDED TO THIS SITUATION.