When removing a tooth you have to pry and loosen the gum around the tooth to remove it. You could have bruising around the sight of the extraction. Or it could be by the injection of the anesthetic that caused the bruising.
I think that it would be possible to bruise your throat, maybe if the dentist slipped. Maybe the back of your throat hurts from having your mouth open for so long.
No usually you do not bruise your throat during a tooth extraction. Your mouth probably was dry or you bit your gums when you were knumb from the extraction that you got.