B737-800
Flight Crew Air Transport Pilot (ATP); Flight Crew Instrument; Flight Crew Multiengine
Flight Crew Last 90 Days 120; Flight Crew Type 12000
Time Pressure; Workload; Human-Machine Interface; Distraction; Communication Breakdown
Deviation - Track / Heading All Types; Deviation / Discrepancy - Procedural Published Material / Policy; Deviation / Discrepancy - Procedural Clearance; Flight Deck / Cabin / Aircraft Event Illness / Injury
Air Traffic Control Issued New Clearance; Flight Crew Became Reoriented
Human Factors; Environment - Non Weather Related; Procedure
Approach briefing: Briefed the TBARR 1 Arrival. Briefed both the ILS 35L and the RNAV Z Runway 35L including the runway transitions. ATIS reported that both were in use. During Arrival descent: was informed by Flight Attendant that a Passenger had difficulty breathing and was being attended to. Told Approach Control (second from the Final Controller) and we were given priority handling and he told us to expect Runway 35L. We confirmed the RNAV-Z 35L in the FMC.  Sent Dispatch a message. Flight Attendant called us numerous times during the arrival transition. The Final Controller told us 'after LDORA; cleared for the ILS 35L. We mistakenly did not execute the ILS 35L in the FMC; which now ended up going from LDORA to CRUPP instead of via the ILS 35L transition fixes. After passing LDORA Approach gave us a 060 followed by a 020 heading to join ILS 35L and cleared for us the approach.Our planning and preparation for the arrival and landing was performed thoroughly. During this high intensity period of time with many non-normal distractions we need to be cognizant when changes take place such as changes to arrivals and approaches and make sure those changes are loaded and executed. We could've also queried ATC of the approach that was being planned for us.  It would've been a great help if ATC; the second from the Final Controller told us which approach to expect instead of having the Final Controller just clear us for the ILS 35L via the transition not too far from LDORA fix.Navigated via wrong transition.
Captain reported navigating on via the wrong transition by executing the RNAV instead of the cleared ILS approach; following an onboard passenger problem.