The man wakes up every morning and looks at his wrist-watch screen that tells him that he feels fine when he doesn't. A lump begins to show on his forehead that grows daily and eventually becomes like a unicorns horn. He eventually breaks away from his society and I think even meets a woman with the same condition so has a happy ending... I think. I might be confusing the ending, it's been a while. I read it maybe 30yrs ago but I'm fairly sure it was written in the 50's for some reason. Cheers
Found someone else looking for it: https://www.goodreads.com/topic/show/2029851-solved-man-slowly-transforms-into-unicorn-you-are-ok-you-are-not-ok
Solved as "Mythological Beast" by Stephen Donaldson of Thomas Covenant fame. Link in comments below...
Not much of a summary, but what I found (from Best of Stephen Donaldson)
I will skip lightly over ‘Mythological Beast’ which was a slight story about a man in a safe, secure future world turning into a unicorn. Deftly handled but basically silly.
I rememembered reading it and couldn't recall the circumstances, but I know I read Daughter of Regals which contains it.