All vaccines, including the COVID-19 vaccines, can have side effects. In general, these are mild and short-lasting side effects, and the authorities consider the vaccines to be very safe and well-documented vaccines.
Most people experience some pain where they are injected. Other common side effects include fatigue, headaches, muscle and joint pain, chills, a slight fever, and redness and swelling at the injection site. These are generally signs that your body’s immune system is reacting as it should to the vaccine. You do not need to call your doctor if you experience these known and short-term side effects.
In rare cases, severe allergic reactions (anaphylaxis) may occur, caused by e.g. allergy to something in the vaccine.
If you have previously had a severe allergic reaction after receiving a vaccine or injection, you should contact your doctor before you are vaccinated against COVID-19. If you have a known allergy to macrogols/PEG/polyethylene glycol, you should not be vaccinated with Comirnaty from Pfizer/BioNTech, COVID-19 Vaccine Moderna or Vaxzevria from AstraZeneca. Emergency staff will always be on hand to deal with rare allergic reactions at the COVID-19 vaccination centres.
From other vaccines, we know that almost all vaccination side effects occur within the first six weeks of being vaccinated. It is very rare for them to occur later. Both the Danish and European medicines agencies monitor vaccines closely after they have been approved, both in terms of how well they work and how many side effects they cause.
See the Danish Medicines Agency’s page on reported side effects of COVID-19 vaccines