BE95 PLT BECOMES DISORIENTED DURING ILS APCH TO AND DSNDS BELOW DA AFTER INITIATING THE MISSED APCH.

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TRAINING FLT IN MY ACFT; A B95 TRAVEL AIR DEPARTED VFR CLR SKIES FOR SINGLE ENG APCHS ILS RWY 35L INTO ZZZ2. AFTER 2 APCHS MY INSTRUCTOR AND I DECIDED TO FLY TO ZZZ FOR FUEL BEFORE RETURNING TO ZZZ1. WE CHKED THE AWOS AND ZZZ RPTED 200 FT OVCST 1 1/2 SM VISIBILITY. WE ELECTED TO PICK UP IFR CLRNC WITH APCH CTL. WE ASKED FOR ILS APCH TO ZZZ AND WERE GIVEN VECTORS. AFTER BEING CLRED FOR THE APCH I INTERCEPTED THE LOC AND THEN THE GS. I DID NOT HAVE THE ACFT CONFIGURED FOR LNDG AT THE FAF. GEAR WAS DOWN BUT I CONTINUED ADDING FLAPS. AT ABOUT 1700 FT MSL WE ENTERED THICK FOG. I FOLLOWED THE ILS APCH AND CONTINUED DOWN LOOKING FOR 697 DA. AT ABOUT 1100 FT MSL I BECAME DISORIENTED AND WAS EXPERIENCING VERTIGO. I WAS BELOW THE GS AND HAVING TROUBLE WITH MY SCAN. AT 750 FT AGL I CALLED FOR MISSED APCH AND APPLIED FULL PWR AND RETRACTED THE FLAPS AND GEAR. I DIDN'T KNOW IT AT THE TIME BUT I CONTINUED TO DSND BELOW THE DA AND MY INSTRUCTOR LATER SAID I WENT DOWN TO 600 FT MSL. I LOOKED UP AND SAW AMBER LIGHTS DIRECTLY IN FRONT OF US AND PULLED BACK ON THE YOKE FOR A POSITIVE RATE OF CLB. I MAINTAINED CTL OF THE ACFT AND CONTINUED TO CLB OUT OF THE FOG AND CONTACTED ATC TO INFORM THEM WE HAD GONE MISSED APCH. WE CONTINUED DIRECT TO ZZZ1 AND REQUESTED THE GPS/RNAV INTO ZZZ1. THE REMAINDER OF THE FLT WAS UNEVENTFUL. NOT HAVING THE ACFT CONFIGURED FOR LNDG AT THE FAF AND CONTINUED FLT INTO LOW IFR RESULTING IN SPATIAL DISORIENTATION AND VERTIGO CAUSED ME TO DSND BELOW DA ON THE ILS APCH INTO ZZZ.