I had to look on Google about ommetaphobia. Yes, this is close to what I meant, but still a bit far. I don't have a phobia of eyes, but only of the fact other objects are getting close to an eye.

I definitely have on: fear of cliffs (cremnophobia).

Is it only cliffs, or is it related to some fears of height (which is actually well spread if I am not wrong).

I think in my case it might be very directly connected to the fact that my brothers tossed me off a cliff (yes!) when I was very, very young

What?! Kids are sometimes... well... you know ;) But this clearly explains your phobia (who may not be genetic at all).