Your description sounds just like "Counter-Clock World" (1967) by
Philip K. Dick.
"[The] world has entered the Hobart Phase--a vast sidereal process in
which time moves in reverse. As a result, libraries are busy
eradicating books, copulation signifies the end of pregnancy, people
greet with, "Good-bye," and part with, "Hello," and underneath the
worlds tombstones, the dead are coming back to life. One imminent
old-born is Anarch Peak, a vibrant religious leader whose followers
continued to flourish long after his death. His return from the dead
has such awesome implications that those who apprehend him will very
likely be those who control the fate of the world."
Longer summaries and reviews can be found at:
Counter-Clock World at PhilipKDick.com
Andy's Anachronisms - Time Travel Book Reviews: Counter-Clock World
The following book might also be a possibility:
"Ubik" (1969) by Philip K. Dick
"This novel is a metaphysical comedy of death and salvation (which is
available in a convenient aerosol spray). (...) As the story
progresses, time moves backwards as the characters remain in their
current time period. This makes for some very clever situations as
objects deteriorate before their eyes and a world from the past
Arguably, Philip K. Dick is a "megastar" of Science-Fiction, but I
hope this is what you are looking for!
(I read the book "Counter-Clock World")
"Philip K. Dick" [at Amazon.com]
"time moves backwards"