KING AIR PILOT REPORTS MISSED APPROACH AT HOU AFTER FAILURE TO DESCEND IN A TIMELY MANNER ON THE GS. MISSED APPROACH HEADING ASSIGNMENT IS NOT HEARD CAUSING CONFLICT WITH B737.

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THE PLT WAS ENRTE TO HOUSTON HOBBY ARPT ON APR/WED/07 AT APPROX XA30; AT 3000 FT MSL VIA RADAR VECTORS TO INTERCEPT THE LOC FOR THE ILS APCH TO RWY 4. A VECTOR WAS RECEIVED FROM THE APCH CTLR TO 'MAINTAIN 3000 FT TILL ESTABLISHED ON THE LOC; CLRED FOR THE ILS APCH TO RWY 4.' THE PIC DID NOT MANAGE THE DSCNT OF THE ACFT SUFFICIENTLY TO BE ABLE TO INTERCEPT GS AND COMMENCE THE FINAL APCH; AND WAS PROMPTED BY THE CTLR TO STATE INTENTIONS; IE; 'YOU ARE ABOVE GS; DO YOU WANT TO EXECUTE A MISSED APCH?' THE PLT EXECUTED A MISSED APCH BECAUSE THE ACFT WAS TOO HIGH TO CONTINUE A SAFE AND STABILIZED APCH. THE APCH CTLR ISSUED A 'R TURN' AND 'MAINTAIN 3000;' BUT THE HDG WAS NOT HEARD OR ACKNOWLEDGED. THE PLT'S ATTN WAS FOCUSED ON EXECUTING THE MISSED APCH AND ON THE TRANSITION FROM A DSCNT IN THE LNDG CONFIGN; TO A CLB TO 3000 FT. THE PLT EXECUTED THE R TURN AND ESTABLISHED A SW HDG (APPROX 210 DEGS) AND WAS AWAITING AN OPPORTUNITY TO CONFIRM THE HDG WITH THE APCH CTLR; BUT AS THE PLT CAN BEST RECALL; DUE TO RADIO CONGESTION ON THE FREQ NOW DUE TO THE NECESSITY TO RE-SEQUENCE THE KING AIR AND FOLLOWING TFC; NO CONFIRMATION CALL WAS MADE TO THE PLT. THE FIRST CONFIRMATION THE PLT HAD OF AN INCORRECT HDG WAS WHEN THE CTLR DIRECTED A L TURN TO 170 DEGS; AND STATED 'YOU TURNED 50 DEGS TOO FAR.' THE PLT OF THE KING AIR WAS STILL ATTEMPTING TO ESTABLISH A CLB TO ASSIGNED ALT AND DUE TO THE IMPERATIVE TONE IN THE CTLR'S VOICE; TURN THE ACFT TO THE CORRECT HDG. THE PLT OF THE KING AIR ALSO HEARD IMPERATIVE HDG CHANGES ISSUED FOR AN ACR Y FLT. THE PLT OF THE KING AIR WAS REQUESTED TO CONTACT THE HOUSTON APCH CTL SUPVR; AND WAS INFORMED OF THE NEAR MIDAIR AND THAT A PLTDEV RPT WOULD HAVE TO BE ISSUED. THE PLT LATER LEARNED THAT HIS REAR CABIN PAX HAD VISUALLY SEEN 'A RED LIGHT' ON THE ACR Y JET IN CLOSE VICINITY TO THEIR ACFT. THE HUMAN PERFORMANCE FACTORS THAT CAUSED THIS INCIDENT WERE: 1) THE PLT DID NOT DSND THE ACFT IN A MANNER THAT ENABLED HIM TO SAFELY INTERCEPT GS AND CONTINUE THE ILS APCH; AND HAD TO EXECUTE A MISSED APCH. 2) THE PLT DID NOT ACCURATELY HEAR THE ASSIGNED HDG ON THE MISSED APCH. 3) THE PLT DID NOT SEEK CONFIRMATION OF THE ASSIGNED HDG BECAUSE: A) TASK SATURATION IN THE COCKPIT WHILE RECONFIGURING THE ACFT FROM A GEAR/FLAPS DOWN DSCNT TO A GEAR/FLAPS UP CLB. B) SUBSEQUENT CONGESTION ON THE APCH CTL FREQ DUE TO THE FACT THAT HE BOTCHED THE APCH CTLR'S ACFT SEQUENCING PLAN. 4) THE PLT TURNED THE ACFT TO AN INCORRECT HDG AND IN IMC CONDITIONS DID NOT SEE THE IMPENDING TFC CONFLICT.