Thanks to Julian and Chris for first bringing this to my attention when it occurred!
The short of it was that every time an image was displayed, the server was getting the image dimensions on the fly rather than from the database. This has always been the case, but with the high traffic, it overloaded my share of CPU time. I think I'll change how that's handled. For now, I've just set a standard display size of the page section, so images might not look quite right on the site. They will download correctly, though.
This isn't at all a complaint against my site host, (HostGator) they could have dropped access to the whole site and never said a word. I actually got a phone call from one of their techs letting me know what was going on.
I'm sure some will ask why I don't have a dedicated server to run it on. The short answer is funding. The highest ad payout day for this site to date is under $6 and most days, it's less than a tenth of that. We might get swamped with visitors once a month like this, so the investment isn't worth it at the moment.