I would very much doubt that it’s the injection site that hurts today. I always have multiple shots of pain killers (more for work on the upper jaw than the lower), partly because the dentists that I use tend to be ultra-conservative about using too much pain killer (whatever they use) and it takes a long time to have the desired effect on me.
But I’ve never, ever, had pain the day after a dental procedure from the pain killer injections. Not once. Residual pain from the procedure, oh yes! but never from the injections.
When you had the fillings, did the dentist take care that none of the new fillings is interfering with the occluding tooth when you bite together? By that I mean, does any part of a tooth now touch its opposite tooth because of the filling, and where it didn’t touch before? That can cause a lot of pain, if the dentist left a “proud” tooth, even if it seems like an insignificant touch.