C182 PLT BECOMES DISTR BY PAX MEDICAL CONDITION AND LANDS ON WRONG RWY AT DFW. FURTHER DISORIENTATION LEADS TO TXWY INCURSION WHILE TAXIING TO RAMP.

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I WAS FLYING FOR AN EVENT FOR DISADVANTAGED CHILDREN AND THEIR PARENTS. WE WERE USING RWY 13L FOR THE EVENT AND THE PARALLEL RWY (RWY 13R) WAS IN USE BY ALL OTHER TFC; INCLUDING ACR'S. DURING MY TRANSITION FROM L BASE TO FINAL; I BECAME DISTR BY THE CHILD IN THE R FRONT SEAT WHO BEGAN TO SHOW SIGNS OF DIFFICULTY WITH HER BREATHING. I BECAME INVOLVED WITH HOLDING HER HEAD BACK TO TRY AND RESTORE HER BREATHING. DURING THE DISTR; I OVERSHOT RWY 13L AND LINED UP FOR FINAL ON RWY 13R BY MISTAKE. THE TWR ASKED ME TO CONFIRM THAT I WAS CLRED TO LAND RWY 13L; WHICH I CONFIRMED. DURING SHORT FINAL; IT FINALLY REGISTERED THAT I WAS LNDG ON THE WRONG RWY. THE TWR INSTRUCTED ME TO CLR THE RWY QUICKLY BECAUSE THERE WAS A B737 ABOUT 1/2 - 3/4 MI OUT ON FINAL APCH TO RWY 13R. I LANDED AND CLRED THE RWY USING A HIGH SPD TXWY. THE B737 EXECUTED A NORMAL LNDG WITHOUT HAVING TO GO AROUND. I WAS THEN CLRED BY GND CTL TO TAXI TO HOLD SHORT OF RWY 13L; WHICH I DID. I WAS THEN CLRED TO CROSS RWY 13L AND BECAME DISORIENTED AND USED THE INCORRECT TXWY ON THE OTHER SIDE OF THE RWY. DURING THIS TIME; I WAS STILL INVOLVED HOLDING THE CHILD'S HEAD SO SHE COULD BREATHE WITHOUT DIFFICULTY. HER FATHER WAS HELPING FROM THE BACK SEAT; DIRECTLY BEHIND THE CHILD. WE TAXIED TO PARKING WITHOUT FURTHER INCIDENT. PRIOR TO THE FLT DURING THE PAX BRIEFING; THERE WERE NO DIFFICULTIES NOTED WITH THE CHILD'S POS IN THE SEAT. DURING THE FLT SHE SLIPPED FORWARD IN THE SEAT AND IT WAS THIS NEW POS THAT CAUSED THE DIFFICULTY WITH HER BREATHING DURING THE CRITICAL LNDG PHASE. HER FATHER SPOKE PASSABLE ENGLISH; BUT HER MOTHER ONLY SPOKE SPANISH. THIS COM DIFFICULTY PROBABLY CONTRIBUTED TO MY NOT UNDERSTANDING AS MUCH ABOUT THE CHILD'S DISABILITY AS I SHOULD HAVE PRIOR TO DEPARTING THE ARPT.