Thanks to all for the input!
This is definitely the flu, a viral thing. Knowing that, I am a minimalist when it comes to drugs, especially anti-biotics. As others pointed out, they would help only for secondary, bacteriological, infections.
I suspect that, though my nose seems clear, that some of the upper sinuses are plugged. When those clear out, life (and sense of smell) will be back to normal.
In the meantime, the lack of an appetite makes for a pretty good diet. I've lost 19 pounds!