L.A.
This is very normal. He just has no way of communicating that he is frightened, nervous, uneasy and just needs to be comforted.
This would have happened even without the shot. It is their age.
Just keep doing what you are doing. Hold him and speak calmly. Try to distract him and stay as calm as possible.
It is a phase. Some children will always be shy or have trouble in transitions that are unfamiliar and some kids will go with the flow.. It is their individual personalities.