Yes, this is normal. Vaccines are designed to give you immunity without the dangers of getting severe disease. It is common to experience some mild-to-moderate side-effects when receiving vaccinations. This is because your immune system is instructing your body to react in certain ways: it increases blood flow so more immune cells can circulate, and it raises your body temperature in order to kill the virus.
Historically, when new vaccines are introduced, unknown side effects occur within 2 months of vaccination, if there are any. We continue to monitor safety even after a vaccine becomes available to the public.