Turns out the thing on my leg (don't worry, I won't post pictures) is in fact shingles, and not a bug bite.
Anecdotally, my wife says that from her office's experience, there has been an uptick in outbreaks of people who experience cold sores and an increase in shingles outbreaks after the vaccine, possibly because of the stress it puts on the immune system.
For me, that's the second shingles outbreak I've had in under 3 years, so my PCP will give me a prescription for the shingles vaccine, even though it's typically not used until age 50. But you're not supposed to get the vaccine until 3 months after the COVID vaccine, so I've still got a bit.