LOW TIME IFR RATED CFI IN C152 BECAME DISORIENTED WHILE PASSING OVER SLI ON VOR RWY 30 APCH TO LGB. EXCESSIVE CORRECTIONS TO GET BACK ON COURSE CAUSED A TFC CONFLICT TO DEVELOP WITH FASTER MOVING SECOND ACFT MAKING ILS RWY 30 APCH BEHIND HIM. SUBSEQUENT MISSED APCH WAS INITIATED PRIOR TO REACHING THE MISSED APCH POINT.

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I WAS FLYING VFR-ON-TOP WITH AN IFR CLRNC TO FLY THE VOR RWY 30 APCH INTO LGB. I WAS VECTORED; CLRED FOR THE APCH; AND TOLD TO DSND TO 1500 FT MSL IMC. JUST BEFORE XING THE SCI VOR; I WAS HANDED OFF FROM SOCAL APCH TO LGB TWR OVER TOP OF SCI VOR. I HAD FULL SCALE DEFLECTION OF MY CDI; I OVERCORRECTED AND HAD TO GET BACK ON COURSE. LGB TWR INQUIRED ABOUT MY COURSE; AND I TOLD THEM I WAS CORRECTING. SHORTLY AFTER THAT; LGB TWR TOLD ME I WAS S OF COURSE AND TO GO MISSED. THERE WAS A FASTER AIRPLANE BEHIND ME. MY 80 KT SPD WAS A FACTOR AS STATED BY ATC. I EXECUTED A MISSED APCH AT THAT POINT AND TURNED TO 200 DEGS AND CLBED TO 2500 FT MSL. I WAS LATER TOLD I SHOULD HAVE FLOWN TO THE MAP AND THEN EXECUTED THE MISSED APCH. LGB TWR WAS THE CTLING AGENCY THAT TOLD ME TO GO MISSED APCH; AND WHEN I IMMEDIATELY TURNED AND CLBED; NOTHING WAS SAID TO MAKE ME THINK I WAS IN ERROR. I NOW UNDERSTAND THAT SOCAL APCH WAS IN CTL OF ANOTHER ACFT ON THE ILS RWY 30 TO LGB. WE WERE 2 ACFT ON 2 DIFFERENT APCHS FOR THE SAME RWY AT THE SAME TIME; BUT CTLED BY 2 DIFFERENT FACILITIES. ALTHOUGH WE NEVER SAW EACH OTHER; WHEN I WAS TOLD TO GO MISSED; AND DID; MY L CLBING TURN CREATED A CONFLICT WITH THE TFC ON THE ILS. I THOUGHT I WAS CORRECT TO FLY THE MISSED APCH WHEN I DID; BECAUSE OF MY CDI HAVING FULL SCALE DEFLECTION AND LGB TWR TELLING ME TO GO MISSED. I DO NOT THINK LGB TWR WAS FULLY AWARE OF OTHER TFC IN THE AREA UNDER THE CTL OF SOCAL APCH. I DO; HOWEVER; SEE WHERE I MAY HAVE BEEN IN ERROR. I DID WHAT I THOUGHT WAS CORRECT AT THAT MOMENT. I PRIDE MYSELF ON BEING CAPABLE AND PROFICIENT PLT AND CFI.