Had the same thing happen to me a while back. Was cutting rotors on the lathe at work without goggles..
I always stood pretty far back though and never looked real close at it while it was making the cut, just stood back and made sure everything was cutting alright. Took a shower that night and my left eye felt a bit irritated but I thought it was just an eyelash bothering me since it does happen alot. Started gettin worse and I looked harder into my eye to see what was wrong and sure enough, a tiny little piece of metal made it into my eye. I managed to pluck it out with some tweezers lol, takes a steady hand and hard to keep your eye open but I managed after a few tries.
Although I got the piece out, had to go visit the optimologist to pluck out the rust still in there.
It didn't hurt at all though when they took it out and the sooner you get it out, the better because I went right back to work the same day I had them pluck that bastard outta my eye.
I wear those ridiculous looking goggles where it basically leaves a mark all around your eyes when you take it off but whatever will keep that crap out is fine with me. I'm really paranoid still about getting crap in my eye.