It's definitely the parotid, the biggest of the salivaries, just under the cheekbone, in front of the ear.
After the movie, I experienced my latest weird symptom: very salty-tasting saliva, but only on the right side of my mouth, on the top. Extensive Googling turned up this article, RadioIodine and Your Salivary Glands. This article is a layman's version of a medical journal article I had found earlier. I would've had to shell out $44 to read the real deal, and probably would've only understood half of it, so I was very glad to find the summary.
Key grafs which I'm trying not to freak out over (emphasis added):
In most cases, immediately after high doses of radioiodine, the salivary glands, especially the parotid glands, become swollen and painful. Alternately, these symptoms can develop months later. In either case, the effects intensify over time.
(I did have "mumps" during the RAI isolation period.)
Other organs known to concentrate and transport iodine include the gastric mucosa, pancreas, lactating mammary glands, chorid plexus and the ciliary body of the eye.
Have I mentioned that I've been getting a pain under my right rib cage, off and on, recently? I was thinking it was just adhesions or scarring from my gallbladder surgery last year, but now I'm trying not to think about what else it could be.
Anyway, I think I will let my endo know that this is happening and see if there is anything she needs/wants (me) to do. If inflammation of the salivaries gets severe, apparently, nerves can be affected and facial paralysis can result (whee!). Wouldn't want that to happen, but I've no idea what, if anything, they can do to treat this or fix any ongoing damage.