It will get you by surprise, top drawer of the bottom cabinet is where my safety glasses reside, so if I am using tools, there is no excuse.
There is a local auto repair shop down the road a couple miles, I remember the owner, 15 years ago or so, had the same thing happen, drill bit broke, he did lose an eye, I forget the circumstances, glad you did not get hurt.
I know the feeling, often times forgot when pulling nails, and have one smack you right under your eye.. so many things that can fly like shrapnel and cause serious injury, 2 things I constantly use, hearing protection and eye protection, I carry a small round case with soft rubber ear plugs, for loud noises, undesirable conversations LOL ! My father, for some reason has this need to clear his throat, had him out for dinner the other night, birthday etc., he did that, thought my eardrums were going to pop, don't know what it is, good hearing, some tinnitus, but darned sensitive ears, always carry those.
Part of my safety meeting/tool talk when I supervised crews in the field included the demonstration or description of an olive with a toothpick through it, a comparison to the human eye, to get a graphic point across about the danger of not wearing eye protection.
The worst thing I would commonly see in the field was someone using a cut off saw, metal blade, cutting bundles of metal studs, no eye protection or hearing protection, the noise alone would make me cringe, not to mention the sparks and abrasive materials that spray out. Saw it on every job, just incredible the risks people take, for the sake of a few dollars worth of protection.