I had an adverse reaction to my second Covid vaccine, but not enough to recommend against getting the vaccine. I had redness, pain and swelling around the injection site the next day and lasted about 5 days. I also had significant fatigue, body aches, and chills the following day. Significant enough to send me to bed. Still, all preferable to actually getting the infection, with a risk of sending me to the hospital or worse!
None of this is considered an allergic reaction, just an immune response.
Jan