YES! Long-term safety is still being studied. The Moderna vaccine trial included approximately 30,000 people 18 years and older in the USA. The Pfizer vaccine trial included approximately 43,000 people 16 years and older in the USA, Argentina, Brazil, and South Africa.
Most side effects happen within 7 days of vaccination and last 1-3 days. More people reported side effects following the second dose.
Some participants had other health conditions during the studies that the FDA believes were unrelated to the vaccines.