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. There are certainly a few glowing testimonials on record...
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. Make sure to rinse with plain water afterwards).
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 cavities (tooth decay) and dental/gingival infections.
1 Information on Dr. Hulda Regehr Clark's body detoxification protocols and Dr. Hulda Clark's instructions for brushing teeth). Also read Hydrogen peroxide against gum disease: a double-edged sword in the fight against gingivitis & periodontitis and the Warning regarding the use of hydrogen peroxide for brushing teeth.