Is it the Doctor's story about his time on the planet that was out of sync with time from the Distant Shores collection? ETA: Eighteen Minutes by Terri Osborne
Whooo! All right, here we go again: "You are being asked for simple medical information, and for the sake of your sick and dying people, you had better supply as much as possible." "That is out of the question," the doctor answered. "And my own personal animosity toward your Federation has nothing to do with my refusal to comply with your abhorrent request." His eyes narrowed. "Since you clearly do not understand my race, I will explain. We are a very private people, human. We do not share with others."
You did get it partially right-the Trek Lit novel the section is from does involve a medical mystery.
I'm afraid I have no idea with this one. I will just pick a book at random. One that I haven't read. My chances of being right are about 0.2%. um Incident at Arbuk?
Hooray, I got one. (And it only took thirteen pages, too.) Here's mine: The overture finished. The opera began, with Geordi running across the stage in his uniform from the other ship, synching with the voice of the tenor singing Tamino, the hero of the opera, something along the lines of "It's after me, it's after me!" He was promptly pursued across the stage by the required Monster, a creature that looked suspiciously like numerous of the staff from engineering operating a hastily cobbled together Chinse "street dragon" made of used blankets from sickbay and a painted waste container for the head. "Tamino" swooned convincingly at the sight of this apparition and fell over. The Three Ladies appeared in the form of Lieutenants Hessan, Renner, and Egli, stunned the Monster with phasers, and began "singing" charmingly about the beautiful daughter of the Queen of the Night, and how Tamino really ought to get together with her. Fictitiously yours, Trent Roman
Wow, and I was sure that one would be a stumper. I bow to you, sir, and hand you the torch. Fictitously yours, Trent Roman