The next time you are planning to get a shot in the arm, do not lift weights for a couple of days prior. Also try to relax you muscle as much as possible. This should lessen the discomfort. We tend to tense up when we know a shot is coming. That makes it hurt more.
You could be sore because of the technique on the part of the nurse who administered the shot. I ran the flu shot clinic at one of the jails I worked in. I also was the clinic RN at a local training facility. I gave the student's their immunizations and Depo-Provera on a regular basis. There is a trick to giving shots in the arm so that they are barely felt.