What are the side effects of local anesthetics?

I don’t mean just the numbing of the nerves, that much is obvious. I mean other effects one might come across.
I just had two of my teeth taken out and the dentist used some… felt like someone had punched me hard in the face and it was swollen, haha. But when I looked in the mirror, it wasn’t.
I was just curious to know what other affects local anesthetic has on the body and/or the mind.