Is blood money obligatory for someone who has a tooth or molar extracted by a dentist when it is causing them pain, by analogy with the principle that blood money is due for every body part that is damaged?

It is stated in the Hadith that for teeth, there are five camels, and it is mentioned in another narration that for a single tooth, there are five camels. All of this pertains to the destruction of a person's organ when the destroyer is not the owner of the organ, and provided that the owner of the organ did not authorize the destruction. Consequently, there is no blood money (diyya) due from someone who extracts their own painful molar or tooth at the dentist, nor is there any due from the dentist.