Food grade hydrogen peroxide & ozone
While ozone for instance has shown powerful healing ability for a variety of complaints including dental cavities, the usefulness of hydrogen peroxide for instant toothache relief is a matter of personal experimentation...
Food grade hydrogen peroxide
Dr. Hulda Regehr Clark (and likely other authors) recommend using a few drops of hydrogen peroxide in water as a mouthwash (not, however, if you have metal in your mouth "because it will leach out some of the metal"). Since hydrogen peroxide oxidises other substances, it seems to help relieve toothache as well (suggested application: hold a capful of 3% peroxide in your mouth [or mix your own solution using a more concentrated hydrogen peroxide and water] for ten minutes at a time as often as needed).1
Dental ozone treatment
Unless you have a home ozonator with attachments that allow treating a tooth, the following is only available in a dentist's office that provides ozone therapy (there may be none in countries such as the US). Ozone therapy is used in some German dental practices as a powerful antiseptic, disinfectant and painless germicidal treatment against caries (tooth decay) and dental/gingival infections.2