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I have vague memories about a novel or series of novels I borrowed from the library as a teenager (1990s). The protagonist was a young woman (pretty sure) who was exceptional. Civilization basically ended (nuclear war maybe). One significant trial she went through involved controlling an orbiting shuttle, trying to dock with a space station (maybe an orbiting Russian weapon?). Then somehow she transferred to a fantasy setting and became a dragon?
Update: A few more details I remember: The story starts out in the USA of the present (meaning the late 80s or early 90s, probably). The protagonist somehow receives early warning or is sheltered from the early parts of the apocalypse (nuclear or biological warfare I think) and goes to space to try to prevent further destruction.