In over-your-head, but worried to stop the appointment and call for help because it will upset the referral agency? Two facts should be instantly clear: 1) your priority is effective communication; and, 2) you my friend need a different referral agency.
Remember these words of hope: sooner or later this appointment will end.
Nothing you do now will change the work you did then.
The appointment ended at 4:17 PM. It is now 2:06 AM, stop picking it apart and go to sleep.
Always be the interpreter with whom you wish to team.
Scrubbing in on a surgery? NEVER not cool!
The worst, most difficult interpreting appointment still beats any other job I can think of!
I learned to read fingerspelling the old-fashioned way; public embarrassment.