ACFT CLBED THROUGH ASSIGNED ALT THINKING THAT THE ATC HAD CLRED THEM TO A HIGHER ALT; BUT CLRNC WAS FOR OTHER ACFT WITH SIMILAR CALL SIGN.

Narrative

X 123 WAS A SCHEDULED PAX FLT BTWN ATL AND CLE. AT THE TIME OF THE OCCURRENCE WE WERE PROCEEDING R-NAV DIRECT TO VXU VOR AND CLBING TO OUR ASSIGNED ALT OF FL290. I ROGERED THE CLRNC AND NOTED MY FO (WHO WAS FLYING THE ACFT) PUT FL290 IN THE ALT REMINDER WINDOW. SHORTLY THEREAFTER; WE WERE ADVISED BY ATC CTR THAT WE HAD XING TFC AHEAD; Y 123 AT FL310 AND WE COULD EXPECT HIGHER WHEN CLR. I ROGERED THAT XMISSION; BUT FAILED TO NOTE THAT MY FO PUT FL310 IN THE ALT REMINDER. CONTINUING OUR CLB; I CALLED 'OUT OF FL280 FOR FL290' AS WE PASSED FL280. WHEN I LOOKED AT THE ALT REMINDER I SAW FL310 AND MY FO SAID WE WERE CLRED TO FL310. I INCORRECTLY MADE THE ASSUMPTION I HAD MISSED THE CLRNC. PASSING FL293; BOTH OF US NOTED THE TFC AHEAD ON THE TCASII AND NOTED HIS ALT AS 1600 FT ABOVE US. THIS SENT UP A 'RED FLAG' AND IMMEDIATELY QUERIED ZTL ABOUT OUR CLRNC TO FL310. THE CTLR STATED 'NEGATIVE MAINTAIN FL290;' AT ABOUT THE SAME TIME THAT WE ACQUIRED THE TFC VISUALLY. I REACHED OVER; RETARDED THE THROTTLES AND TOLD MY FO TO GET BACK DOWN TO FL290. I BELIEVE OUR MAX ALT WAS FL296. IN ORDER TO AVOID A POTENTIAL CONFLICT WE WERE DIRECTED TO MAKE A 90 DEG TURN TO THE R. ONCE CLR OF THE TFC WE WERE GIVEN A HDG TO JOIN J-91 N OF VXU. HAD I NOT BEEN PREOCCUPIED WITH MY OWN PROBS (SINUS HEADACHE AND CONGESTION FROM ALLERGIES) AT THE TIME I MIGHT HAVE CAUGHT THE INCORRECT INSERTION OF FL310 IN THE ALT REMINDER. REGARDLESS; I BROKE MY OWN 'CARDINAL RULE' BY NOT TAKING QUESTIONS OVER CLRNCS OUT OF THE COCKPIT TO THE SOURCE; INSTEAD OF QUERYING OTHER CREWMEMBERS ABOUT A CLRNC. I ALSO FEEL THE SIMILAR CALL SIGNS; X 123 AND Y 123; CONTRIBUTED TO THIS ALT EXCURSION. NOTE: WE DID NOT GET A TCASII ADVISORY (TFC ALERT) OR RA.