Thanks very much to everyone who replied. I'm trying to concentrate on post 1950 stuff. And I'm not too big on plagues and zombies. I'll start with James White because most people named him.Here's the list so far:
James White (Sector General series - 12 books) Various short storiesGreg Bear (Blood Music)
Daniel Keyes (Flowers for Algernon)
Geoff Ryman (The Child Garden)
Michael Blumlein (Tissue Ablation and Variant Regeneration)
Alan Nourse (Star Surgeon, The Mercy Men, Contamination crew, Bladerunner)
Piers Anthony (Prostho Plus)
John Varley (Steel Beach)
T. J. Bass (The Godwhale)
Lois McMaster Bujold The 3rd & 4th of the Sharing Knife series have "major character learning medicine" as a major plot thread
Mikhail Bulgakov's Heart of a Dog.
James E Gunn The Immortals
C. L. Moore & Henry Kuttner); "The Little Black Bag
Elizabeth Moon "ABCs in Zero G".
Bernard Wolfe (Limbo)
And here's what the SF encyclopedia page gave me And it did lead me to a book of short stories called: Great Science Fiction about doctors
Walter M Miller Jr's "Blood Bank" (June 1952 Astounding),
William Tenn's "Down Among the Dead Men" (June 1954 Galaxy),
Cordwainer Smith's "A Planet Named Shayol" (October 1961 Galaxy)
Larry Niven's "The Organleggers" (January 1969 Galaxy; vt "Death by Ecstasy" in The Shape of Space, coll 1969)
Caduceus Wild (January-May 1959 Science Fiction Stories; rev 1978) by Ward Moore and Robert Bradford
Dr Adder (1984) by K W Jeter,
Resurrection, Inc. (1988) by Kevin J Anderson,
Body Mortgage (1989) by Richard Engling
Crygender (1992) by Thomas T Thomas.
The Madman's Daughter (2013) by Megan Shepherd.
Joe Haldeman's Buying Time (1989; vt The Long Habit of Living 1989).
Raymond Hawkey's thriller Side-Effect (1979)
F M Busby's The Breeds of Man (1988),
Thomas M Disch's The MD: A Horror Story (1991)
Charles L Harness's The Catalyst (1980)
Kate Wilhelm's Welcome, Chaos (1983).
Bujold's Ethan of Athos and Falling Free both have strong themes of reproductive medicine and related genetic manipulation.