S.J.
I would think it's more likely an allergic type reaction than an infection. I used to get the same type of thing after TB tests. It would be about the size of a half dollar, red, warm, raised. It always showed up a couple days after the TB test was read. If I put a little cortisone cream on it, it went away pretty quickly. Fortunately, at his age he probably won't be due for any more vaccines for a long time.
Good luck!