GA SMA UNAUTHORIZED PENETRATION OF ORD TCA.

Narrative

I CALLED GND AND ASKED IF I COULD GET A SQUAWK CODE AND A FREQ FOR CONTACT AFTER TKOF. I WAS INFORMED THEY COULD ONLY GIVE ME THE FREQ. UPON TKOF ON RWY 24 I HEADED STRAIGHT OUT TILL ABOUT 2000 FT WHEN I ASKED TWR IF I COULD TURN L AND PROCEED ON COURSE. THE TWR ASKED MY DIRECTION AND I TOLD TWR 090. I SAID I WAS CLBING OUT OF 2.6 TO 9.5 AND COULD I HAVE A FREQ CHANGE FOR FLT FOLLOWING. HE THEN GAVE ME THE SAME FREQ THAT GND CTLR GAVE ME AND I CONTACTED HIM. UPON CONTACTING APCH THEY GAVE ME O'HARE'S FREQ AFTER I ALREADY TOLD THEM I WAS CLBING OUT OF 2.7 TO 9.5. I THEN CALLED O'HARE AND SAID I HAD JUST DEPARTED PWK CLBING THROUGH 3000 TO 9.5. I BELIEVE THAT O'HARE ASKED ME TO IDENT WHICH I DID AND O'HARE SAID YOU ARE INSIDE THE TCA AND TFC WAS 3/5 MI AND I SHOULD MAKE AN IMMEDIATE HARD L AND DSND TO 2500. THEY SAID THE TFC WAS AT 3200. I DSNDED AT ONCE AND MADE THE HARD L. THE TFC WAS A JET WHICH HAD ALREADY CROSSED MY PATH AT ABOUT MY 1 O'CLOCK. AFTER THE L O'HARE SENT ME BELOW THE TCA AND THEN TO ANOTHER APCH WHO THEN HANDED ME BACK TO O'HARE WHO ASKED ME MY NAME AND HOME BASE TO INVESTIGATE. I FEEL TERRIBLE ABOUT THIS SITUATION. I FEEL THAT TWR OR GND COULD HAVE MENTIONED TO ME TO STAY BELOW 2500 FT AS I DID EXPLAIN TO GND THAT I WAS NEW TO THE AREA AND IT WAS THE FIRST TIME THAT I WAS THERE. I ALSO BELIEVE THAT WHEN THERE ARE SATELLITE ARPTS INSIDE OF A TCA OR AN ARSA; GND AT THE SATELLITE ARPTS SHOULD BE MORE HELPFUL IN EXPLAINING HEIGHTS OF A TCA TO MAKE SURE THERE ARE NO MISTAKES. ALSO THERE SHOULD BE A WAY THAT ALL ARPTS IN A TCA OR AN ARSA SHOULD HAVE SQUAWK CODE IN ORDER TO TKOF OR AT LEAST GIVE AN OPTION TO THE PLT IF HE IS UNSURE OR NOT FAMILIAR WITH THE ARPT.