Do anesthetics keep you from feeling all pain?

They can. : But it is more complicated than that.

Not necessarily: The components of "anesthesia"generally include analgesia (pain relief), diminished awareness, lack of movement (to allow surgery to go forward safely) and sometimes, but not always, sleep. An anesthetic that is delivered to you more locally (topical, peripheral, spinal, epidural) will create a "pain-free" zone in a limited location only. So, not "all pain!".

That is the plan: A good general anesthetic will prevent you from being aware of any pain. A spinal or epidural will stop the pain by blocking the nerves so that you can still be awake. Discuss specifics with your doctor.