The book is probably "Rapture" (1996) by David Sosnowski.
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Various descriptions of the book:
"A new virus stalks America - Angelism. It doesn't kill you instead you
grow wings. "
"Premise: a wonderful new virus is sweeping the country, Angelism. It
starts like the flu, turned your skin green, then you sprout wings."
"The overarching story of this book deals with the effects on society when
normal people begin sprouting angelic wings. The story follows two main
characters; Alexander 'Zander' Wiles is a petty crook suffering from acute
agoraphobia, and Cassandra 'Cassie' O'Conner, a psychiatrist specializing
in 'angels' and author of a pop-psychology book titled Angel Blues. Both
live and work around Detroit, Michigan, and much of the story takes place
either in Detroit or its suburbs. "
"Part romance, part allegory, part satire of modern culture, David
Sosnowski's first novel is a wry takeoff on the current New Age angel
phenomenon. Zander Wiles, a small Detroit dope dealer, feels a powerful
itch on his back and soon discovers he's growing wings. The epidemic of
"Angelism" spreads, and in no time Congress has gotten involved, angel
support groups crop up, militant factions create the Feathered Nation, and
America has a new and otherworldly minority on its hands. Zander, the first
celebrity angel, eventually crosses paths with Cassie O'Connor, also a
fledgling semi-divinity, and their romance carries the plot to its manic
close. Sosnowski has a dry, wicked sense of humor, and his descriptions of
angelic movie theaters, bars, and bumper stickers are priceless."
"Spinning an inventive, new riff on contemporary angel mania, Sosnowski's
first novel is a fanciful zeitgeist satire, positing a world in which
ordinary people begin to sprout wings, then become ostracized and victims
of hate crimes because of widespread prejudice against their newfound
ability to fly. A drug-dealer in a ravaged, post-industrial Detroit, Zander
Wiles is the first angel to go public with his new physiology. Ditched by
his partner in petty crime, Wiles becomes a novelty on the talk-show
circuit, until the number of angels across the nation rises, medical
understanding of the phenomenon increases and, due in part to his obnoxious
antics, his fans turn against him. Following a suicide attempt he
approaches fellow angel Cassie O'Connor, a therapist specializing in the
needs of dysfunctional angels. Romance begins to blossom, as O'Connor and
Wiles try to come to grips with the emotional weight of angelism and
physical problems like molting and Penguinism, a disorienting condition
that makes it impossible to fly. Sosnowski's portrait of a separate "race"
of non-divine angels as a social phenomenon, and his strange mix of the
cutesy and the apocalyptic, is original and sometimes clever. But his prose
is often shop-worn and his storyline soon grows so freighted with ideas
(while endeavoring at once to be a love story, a fable about racial
difference and a study in the ravages of addiction) that the novel suffers
a Penguinism all its own. "