Happened to me, one in a million shot into the eye while I was at my wargaming club in NY working on a Battletech figure of all things.
Happily, the ER was a block down, and it was a slowish day, so I got seen in about 45 minutes. Doc took one look, irrigated the eye..did the forcep work, and said you'll be fine. He reminded me they use a variant of CA for minor surgical proccedures, so the danger was low as long as the eye got flushed.