It was very simple and quite inexpensive, actually.
For someone without any insurance that was viable in Europe, my case would seem to be most likely to be a problem. But, given that my cold had not gone away and I had a nagging worry that I could have pneumonia, I figured I'd best get it checked out.
The lady at the tourist information counter called around to find a place nearby for me, and they said they would see me in 15 minutes. I waited 5 more, after which the doctor checked me out to ensure I do not have pneumonia (yet another sinus cold, apparently), gave me a prescription for various symptoms and a backup one for antibiotics should they be necessary, and charged me 24 euros for the whole thing. Two prescriptions cost another 11 euros, and I was on my way.
Feeling much better now, as having climbed up to the castle at which I'm staying today would attest.