If you get chilli in your eyes it can cause damage to your eyes if you do not wash the eyes out to remove the chilli in time.
However as long as you remove the chilli from your eyes by washing your eyes out then the chilli in your eyes should cause no damage.
I've had some chilli splatter up into my eyes while cooking before and it did burn the eyes and made the eyes sting but I washed the eyes out immediately and although I had painful eyes for a day the chilli causes no damage to the eyes.
I would recommend wearing some goggles while cooking greasy foods and chilli that could splatter.
I now wear a pair of safety goggles just to prevent getting hot oil in my eyes or chilli in my eyes and it's well worth it.
Getting hot oil or chilli etc in your eyes is painful.