At the urging of so many of you -- I really am touched by your concern -- Cheryl drove me down to the Urgent Care center. They took my blood pressure and the doctor had a look at me and said that he doesn't think it's a stroke because I have none of the other symptoms (no headache, nausea, paralysis, etc.). Labrynthitis is a strong possibility, in which case the best treatment is rest and waiting it out, because it's usually a viral infection and not easily treated with drugs. There are also signs of dehydration, however, so he's told me to cut one of my blood pressure medications (which is also a diuretic) down in half for a few days, pay attention to my BP closely, and contact my regular doctor, especially if the symptoms don't get any better. Oh, and drink more water.
It's sort of funny that I'd get dehydrated here, rather than on the Colorado trip where dehydration was a constant worry.