IMO (not a scientist), moon dust is basically pulverized glass, only without the benefits of weathering and erosion. So think of lots of microscopic sharp, abrasive, shards of finely pulverized volcanic rock and obsidian. Get that stuff anywhere near a mucous membrane - eyes, nose, mouth, throat - and it’s going to irritate you. At the same time, it’s pretty much intert; well, at least the parts that don’t instantly react to oxygen or humidity that is. My guess is that Schmidt is just a little more sensitive to it, or perhaps he rubbed his eyes with a glove by accident.

And for the uninitiated, it’s well documented that everyone in the lander was physically exposed to moon dust. There was no airlock on the lander, so every excursion resulted in bringing whatever was on the suits right into the cabin. They reported that it “smelled” like burned gunpowder, so they were at least all inhaling the stuff.