Hi.. Can understand your concern.. As per your complain if your child has broken teeth there can be exposure of nerves which are present in the central portion of tooth and when the nerves are exposed to the oral cavity any irritation of the nerves can lead to inflammation of the nerves causing pain.. When the infection reaches below the root apex of tooth there can be pus formation and abscess. The pain can radiate to the whole of the jaw on effected side along with headache and earache.. BUT a swollen pointing finger is not related to the teeth and it can be due to any other infection in the nail bed or ingrown nail or any trauma inflicted over the finger or any bug bite for which you need to consult a physician.. I would suggest you that for dental infections you should consult a dentist and get treated for relief from pain and prevent decay to the permanent teeth by improving the oral hygiene of your child.. Hope this information helps.. If you find the answer helpful please write a positive review and click on find this answer helpful as a token of appreciation.. Thanks and regards.. Dr.Honey Nandwani Arora.