Oh, I've had plenty of experience with these, in all kinds of situations, with and without infection, irritated nerves, etc. what I have learned is that the bigger teeth with more roots require more novocaine. I'm not very sensitive to novocaine, so my dentist always has to use 2 shots at a minimum for me, just for a filling. (I think I metabolize it quickly, too, it never lasts long.). For a molar, i usually need 4 shots. They might be able to start with 3, but guaranteed they will have to stop partway thru and numb me up again. (See, I have reason to suspect I metabolize it quickly.). I just had my front tooth done, got away with 2 shots, but then had to get a third partway thru. .
So, don't be shy about telling the dentist upfront if you need more novocaine. If the nerve is irritated (this can happen without an infection), you will need more novocaine. Irritated nerves are hard to calm down. My dentist usually lightly taps the tooth before starting to see if I can feel anything before she starts. Someone else mentioned a dentist dripping the novocaine directly in the hole. I've had that done, too, often because they cant get any more novocaine in my gums. It works, which is the most important thing.
Not sure if others feel this, but when the novocaine begins to wear off mid-procedure, it kinda leaves in waves. I feel a sort of wave of feeling, like a pulse, that flashes over my lips, nose and chin. That's how I know I'll need more novocaine in about 2-5 min.
Anyway, speak up early, ask your dentist to test the tooth to make sure it is good and numb before starting, and make noise if you begin to feel anything mid procedure.