I most likely read this sometime between the late 1990s and 2010. I have no idea where I would have read it. It might be closer to novella length than a short story. It'd be neat to have it identified so I can find out if the author has written any other stories in this world.
The milieu is a post-disaster world (possibly a limited nuclear war) that is recovering and becoming increasingly populated, centralized and technologically advanced. I believe it was set in a mostly-Mexican-influenced culture on the Pacific coast, extending at least as far north as southern California. The culture the story takes place in is almost neo-feudalistic, patterned somewhat on pre-independence Spanish culture in Mexico. Some early 20th century level technologies exist, but I don't know if they are reconstituted or technological remnants.
The protagonist is a travelling doctor. He is considered a neutral figure in whatever struggles/conflicts are going on, because he has more advanced medicines than anyone else, and because he vaccinates everyone as he makes his rounds. (It's possible that the back story included some military use of germ warfare, since characters in the story seem to know what that is, and it would provide some justification for why a doctor who provides vaccines would be held in high regard.)
He arrives in a town which is under threat from a neighbouring warlord who dreams of setting himself up as emperor. In town he meets with a young woman, almost of marriageable age, who he has apparently be keeping an eye on as she grew up; she is smart, curious, scientific and seems to have a much more modern attitude than her contemporaries.
The warlord is trying to discover, excavate and utilize an underground base where a space-capable human-rated launch system was stored to be kept safe in the event of a disaster. I think there may be an orbital base of some sort still in high orbit, and he plans to use it to threaten possible enemies. When the reach the launch vehicle the doctor releases a bio-war plague that kills the generalissimo's soldiers (and possibly the generalissimo too), which causes the base to be quarantined.
The young woman realizes that no bio-war agent would have lasted so long (100 years?) underground, and guesses that the doctor spread it, and that her "vaccination" was actually to protect against the plague virus. The doctor reveals that he is actually part of a secret society dedicated to trying to guide the recovery of humanity, and promises that he will have her sent to a school that will lead to her joining the society.