Good news! My knee problem is nothing serious. I went to see my regular doctor, who spent about ten minutes looking at my knee and came up with the assesment of "Dunno," and referred me to a specialist.
The osteopath ordered x-rays and examined my knee. No damage to the bones or tendons, and the space between the bones was “perfect.” He diagnosed it as chondromalacia patellae, which is a pain under the kneecap. The underside of my kneecap is not as smooth as it would be in an uninjured one, and that is what is causing the discomfort. He gave me a “return to running after injury” program to follow and said that, given my level of fitness, I should start with week 3, rather than week 1. He also gave me a handout of weight training to incorporate into my workouts once I’m back up to speed. This will strengthen the muscles and hopefully prevent a recurrence.
I had my first "return to running" workout last night. I ran 15 minutes at a snail's pace (around 12 minute miles), and it felt really strange to be going so slowly, but hey, better that than hurting myself. After that, it was 20 minutes at a "medium" pace, which I had as 10 minute miles. I am happy to report that when I was done, I only felt mild discomfort in the knee, which was gone by the time I went to bed. Yay!
One of the most delightful aspects of my appointment was that the doctor kept referring to my excellent muscles and skeletal structure, my strong conditioning, and referring to me as a strong athlete. That was really flattering.