PLT OF AN SMA SEL ON AN IFR TERMINAL ENRTE FLT AT A LOW ALT WAS CAUGHT IN A SEVERE TSTM CAUSING HIM TO GAIN AND LOSE ALT FROM ASSIGNED. IN ADDITION; ATC HAD NOT HANDED HIM OFF TO THE DEST TWR CAUSING HIM TO INADVERTENTLY ENTER CLASS C AIRSPACE WITHOUT ATC ACCEPTANCE. FURTHERMORE; HE HAD A CONFLICT WITH A CESSNA 172 APCH AT THE SAME TIME AND WAS SENT AROUND TO AVOID THAT ACFT.

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FLT DEPARTED TPA-SRQ; 2600 FT ALT ASSIGNED; RVR TO SRQ PRETTY POOR WX; TSTMS MOVING IN OFF THE GULF. I WAS GIVEN A 120 DEG HDG FOR WX; THEN 180 DEGS FOR APPROX 30 NM. DURING THIS TIME; SRQ WX TURNED VFR WITH TSTMS MOVING TO THE NE. ABEAM SRQ AT 20 NM PLUS 2600 FT MSL; I WAS NOW IN THE CLR (BELOW CEILINGS AND OUT OF RAIN) AND COULD SEE ABOUT 7 MI W (TOWARD SRQ). SINCE GIVEN THE 180 DEG VECTOR THE CTLR (TPA APCH) HAD NOT SAID ANYTHING TO ME. I REQUESTED AND WAS GIVEN A TURN TOWARDS THE ARPT (260 DEGS). I WAS NOT TOLD THAT A LEVEL 4 TO 5 TSTM WAS BTWN MYSELF AND ARPT. UPON PENETRATION; TURB WAS SEVERE; UPDRAFT TOOK ME UP TO 3200 FT AND THEN A SHEAR TOOK ME DOWN RAPIDLY TO 1500 FT MSL. I POPPED OUT THE SIDE OF THE STORM; UNABLE TO TELL APCH ABOUT THE EXCURSION; BECAUSE HE WAS TALKING TO OTHER ACFT; AND I WAS FLYING THE AIRPLANE. TOLD TPA APCH THAT I HAD SRQ IN SIGHT AND WAS GIVEN THE VISUAL APCH (ABOUT 12 NM FROM SRQ AND I WAS STILL AT 1500 FT MSL). I WAS NEVER GIVEN TO SRQ TWR AND AT 5 NM OUT I ASKED TAMPA TO SWITCH AND WAS GIVEN TO SRQ TWR. UPON CHANGING FREQS; THE TWR WAS ADVISING ANOTHER ACFT OF TFC INSIDE 1 MI SEPARATION; SAME ALT AND CONVERGING. AS SOON AS THE OTHER ACFT ACKNOWLEDGED; I CALLED TWR AND TOLD HIM WHO I WAS. HE HAD BEEN TRYING TO CALL ME FOR THE PAST 10 MI; TAMPA APCH HAD NEVER GIVEN HIM A HDOF AND HAD NO IDEA I WAS IFR HANDLING ON A VISUAL APCH. I CALLED THE TWR ON THE GND AFTER LNDG; I HAD TO CIRCLE TO LET THE OTHER ACFT (A C172) AND APPARENTLY I WAS THE SECOND UNANNOUNCED HDOF THE TPA CTLR HAD GIVEN SRQ TWR THAT MORNING.