If you are cutting your gum from the fractured wisdom tooth it is certainly possible for you to have soreness in the throat area. You should consider having the wisdom teeth extracted.
the teeth, if they are chipping, are probably decayed. Additionally, they are causing your gums to be inflamed. I would not jump to the conclusion that your sore throat issue is due to the wisdom teeth scenario, but I guess it's possible. Why dont you have the teeth removed and see if your sore throat problem clears up?