Both myself and my wife have always had some discomfort or mild side effects from both flu jabs and covid jabs. The sore arm can easily be caused by the person administering the injection either because they hit a nerve or just badly inserted the needle. I had quite a noticeable swelling on the injection site for my first covid jab but it was administered by a doctor and doctors have a generally bad reputation for the ability to inject, my second covid shot was painless but that was a nurse who had probably given more injections than that doctor had hot dinners! None of this would put us off having vaccines.
Stuart