Oh dear
These things happen, although they never should.
You should always wear goggles for any grinding - either angle-grinding, bench-grinding, belt-linishing or whatever. You should wear them at the drill press too and when working on lathes, though I rarely do with these latter two.
I have a good pair of wrap-around grinding glasses that I like, with rather large bug-eye lenses. They're convenient because you can flip them up onto your head like celebrities do with sunglasses - that way you're not always looking for them because you forgot where they are. That's always when you decide to skip using them and get something in your eye.
I've had about 25 (?) bits of metal (and grindstone particles) in my eyes over 28 years. Probably twenty eight bits then. Maybe even 56. About 6 or 7 of them have ended up at hospital because I couldn't dig or flush them out. A few of them (only a few) have been removed quickly with an iron will and a steady hand. I've used moistened cotton buds and carefully sanded matchsticks, softened in water. Lots more have stayed in hours and usually overnight (uncomfortable) but if you're lucky they flush out with tears and early morning eye moisture. Much beyond that and you're off to hospital. There, they dig out it with a big needle! So wear goggles.
If it's a tiny piece of grindstone, or aluminium or anything else non-ferrous, then it's non-magnetic. I don't know if that's worse but I always think it is. Magnetic needles at hospital surely? Oops, it's aluminium. I once had a piece of aluminium in my eye that somehow came out immediately at hospital or just before I arrived. But it left a stain on the retina from oxidation and it looked like there was still something there. They were scratching away at my eye with a needle - at nothing!
I reckon that virtually every occasion where I've skipped goggles and ended up with an eye particle, is because I forgot where I put them and I can't find them, and you're in the middle of a job and you want to crack on.... Of course I have more than one pair and they're scattered about but somehow when you're looking for some.....! Better to keep a pair on your head, where you can.
Never wear gloves working on a drill press or a lathe or anything else rotating. Other than those latex gloves maybe.
Always wear a welding gauntlet (on the non trigger hand) and a full face shield if using one of these fairly modern wire cup brushes for the angle grinder. They are a fearsomely effective tool for de-rusting, and even polishing a little. They spin a lot faster than the equivalent wire cups for a hand-drill and are more brutal. I use one a lot on fresh forged iron while still black hot. But they can easily kick back or run away because you tend to be rotating them about into all the nooks and crannies and different planes and a second across your hand or into your face would be critical. Even a standard glove might not be enough and the wrist is bared too. A big red welding gauntlet is better. Goggles are not enough either. The wires that come off them, now and then, also would ruin an eye. These are one of the most dangerous common tools about now and I've seen them used nonchalantly. They have a far bigger danger of kick-back than even an angle grinder as standard - with a grinding disc fitted.
Never do arc or MIG welding without a full face shield. TIG welding even more so. It will fry your face. Chest and neck can be badly sunburnt too, especially in summer and so with looser clothing. Or in rocket-stove workshops at 25 degrees C.
Good condition cotton overalls are best, with good fastening ability up to the neck. You don't have to have them fastened up all the time, but when welding, it's not a big deal to do so. Lots of pockets too. A good pair that you keep washed regularly should last a couple of years at least.
Wear goggles. Be careful with those wire cup brushes on the angle grinder.