It is extremely unlikely you will experience serious side effects that could cause a long-term health problem after getting a COVID-19 vaccine.
Long-term side effects following any vaccination are extremely rare. In the past, vaccine monitoring has shown that if side effects are going to happen, they tend to happen within six weeks of receiving a vaccine dose.
For this reason, the FDA required each of the authorized COVID vaccines to be studied for at least eight weeks after the final dose. As of February 7, 2022, of the hundreds of millions of Americans who received the vaccine, there have been only 4 cases of serious types of adverse events following COVID-19 vaccination, with evidence that suggests a link to certain types of COVID-19 vaccinations.
Please note, the number of vaccinations and reports of potential health events changes daily. For more current data, please refer to the the CDC's Adverse Events After COVID-19 Vaccination report at https://www.cdc.gov/coronavirus/2019-ncov/vaccines/safety/adverse-events.html.
SOURCES:
https://www.cdc.gov/coronavirus/2019-ncov/vaccines/safety/safety-of-vaccines.html (CDC)
https://www.mayoclinic.org/coronavirus-covid-19/vaccine-side-effects (Mayo Clinic)
https://www.mayoclinic.org/diseases-conditions/coronavirus/in-depth/coronavirus-vaccine/art-20484859 (Mayo Clinic)