Hi Shia,
This sentence is about wearing glasses rather than contact lenses. "Wire-rim" describes the design that is a thin metal frame around the lenses of the glasses. Pull up an image of John Lennon wearing his classic "wire-rim" glasses. The use of the verb "perched" just means that the glasses were resting or positioned on his nose. We also frequently use the verb "perched" to describe birds resting on a branch of a tree. And it sounds like the character described in this sentence was very recently wearing his contacts since contacts can often make our eyes red and uncomfortable. Poor guy!
Please, let me know if this did or did not help you.
Cheers,
Ellen