Call your doctor. A reaction like this is one of the possible side effects. I would not rush off the ER unless it get significantly worse or unless your doctor tells you to
Take him to the ER this will get worse, babies have been having this reaction to vaccines a mom on YouTube her little boy who is 2 or 3 had this same reaction I’m pretty sure they said that it was hives but to be sure I’d take your little one to the ER because yours is a lot younger then that little boy is.
I want to say yes.. I can’t remember with my boys. Did the doctors tell you anything? With most of theirs the doctors always said something like “they might get a bump” or something. Just keep an eye on it and if your concerned, call the pedi and ask what they want you to do