In the U.S. you can report the incident yourself. Use the FDA's Vaccine Adverse Event Reporting System (VAERS). About 7% of incidents reported to VAERS are reported by vaccine recipients or their parents or guardians, according to the FAQ:
It's still a good idea to get your health care provider to help you fill out the report form. This also servers to assure you that your provider knows about the incident. It is unclear how efficient is the flow of information from VAERS back to health care providers.