I have a phobia of things near my eyes?

Women shake hands with men.

It is normal to want to protect your eyes.
Wear some clear glasses for safety.

Preserve it if you are adamant.

Not wanting things near your eyes is not a phobia, its common sense! I personally don't want a flaming hot needle within half an inch of my eyes!

You have eye lids and eye lashed they're defense mechanisms that will protect your eyes from almost anything. Don't worry just try to overcome the fear so it doesn't hinder you.