AskAlice, I've removed them from my face with a needle - by breaking into the top from the side - but, as yours is so close to your eye, it's just too risky, so please don't! Plucking the eyelash should be fine. I'm thinking that they only fall out when another is growing.
They have a tough top layer that keeps the solid white ball (of cholesterol perhaps?) firmly in place. Just 'popping' wouldn't allow it to escape. It's more of a 'slicing then squeezing' exercise, which is why I suggested the GP.
Ideally, you should leave it to resolve itself, though, as it won't be there for ever.