I am trying to describe a situation where a particular color is too bright or harsh. But I don't think 'bright' and 'harsh' are the right words to use here. Is it right to replace the phrase 'too bright' with 'shouty'?
There are more idiomatic ways to tie colors to adjectives of loudness.
Loud as visual description:
loud 1.2 Vulgarly obtrusive; flashy. - ODO
"Shouty," in this context, can mean whatever you want it to mean. It is not a generally accepted adjective in this sense.
If I read it used to describe a person, I'd understand that they were loud and brash, and possibly argumentative or with a short temper.
I'd probably have to think twice to understand what it meant with regards colour, but I could guess what it would mean.
Why not try "loud" or "brash" in this context?