Thanks for the tips! The pain was not very severe; I had no idea I was spending $600 on X-rays until I got the bill... gotta love our health care system. The pain was only severe enough to make cycling no fun anymore, which was more severe than I wanted it given that cycling is currently my full-time occupation. But I've gotten a lot of rest the last 5 weeks, and the pain is now almost entirely gone.
Specifically, I was having dull but increasingly sharp pain at the top, inner corner of each kneecap (i.e. left on the right knee, right on the left knee) when I would pedal, and that spot on each knee was also sore to the touch. I saw a chiropractor in Richardson, TX who sold me clip pedals (I had gone over 2000 miles with regular pedals and shoes!) and showed me the "biodynamically optimal" adjustment for my recumbent seat. Unfortunately, though this may have improved my knee pain (hard to say), it created a strain on my achilles tendons and hips that hadn't been there before, and by the time I reached Austin I was having trouble walking, let alone riding. Although the achilles pain was most acute, I was most worried about the hips because the pain there felt like it was in the actual joints.
Hence the $600 in X-rays: ankles, knees, and hips. But they showed no damage to the bones or cartiledge, which is great news. The stretches the second chiropractor gave me to do (I was also doing no stretches for 2000 miles!) feel good, whether or not they help.
Some friends have recommended ibuprofen, which the orthopedist prescribed in the form of Motrin, but he cautioned that a painkiller could allow me to continue doing harmful activities that I would otherwise know to stop. I'll check into this arnica gel you recommend.
Meanwhile, rest seems to have been the best medicine. I've had almost no pain the last few days, so I should be able to leave Austin on schedule!