It could be like you said a random blip, and now the vaccine has raised your blood sugar, it certainly did mine, after an initial crazy dip. I'd normally say do a basal check, but it's probably not going to tell you a lot at the moment, having had the vaccine. Maybe try increasing your basal a little bit more, if you're happy doing that, and correct with bolus during the day for a week, and then do a basal check.
What basal insulin are you using, and do you split it, or give it once a day?