You may have a dry socket. This is quite painful as the blood clot that protects the bone of the socket has become dislodged, exposing the bone inside. This is not an infection and will eventually heal on its own, but is very painful. Your dentist can place a sedative dressing in the hole to stop the pain and encourage faster healing. Outside of taking over the counter pain medication, there is not much else you can do from home.
You also may have a retained root tip if the dentist did not get all the tooth out or you may have an infection. Both these will also require a visit back to the dentist as you will probably need to be placed on antibiotics.