After considerable effort and no small amount of driving, I have tracked down some Pinworm medication and gotten it into Secondborn. I'll give his brother a dose this evening as well, just to be safe. The plan, as given to me by their pediatrician, is to wait a week after that and then give them another dose.
Meanwhile, Secondborn has developed some kind of rash, primarily on his face, so I've also given him some Benadryl. He coughed hard enough and long enough to make himself throw up last night, so he's at home with me today. It's like a perfect storm of maladies. For the moment, I've asked him to stay out of the back yard and away from the fence beside the creek when he's playing outside at school. (The rash is mainly on the exposed portions of his body, and I'm suspicious that he may have brushed up against poison ivy or something similar.)
Right now, he's building a new Lego set and generally sounding pretty chipper, albeit with occasional coughs, so with any luck we're on our way back out of this.