Numbing injection for lower molar caused intense pain--is this typical?

I went to the dentist the other day for a filling and a tooth extraction, one behind the other. I was numbed first with no issue. The dentist asked if I could feel air on the tooth that needed extraction and I said yes so he then said he needed to administer another injection. He said I may feel a pinch/sting and I said okay, go for it. When he injected the second one I didn't feel a pinch or a sting, it was an intense, burning, stabbing sensation I felt through my entire mouth, head and body. My body jerked, I pushed his arm out of the way and stared shaking and crying. I couldn't go through with it. I've had fillings done before on a few of my molars years ago when I was younger but I cannot for the life of me remember it being THAT painful. I'm thinking about going to another dentist that offers nitrous oxide. Is that feeling normal or did something go wrong?