We give all of our own shots every year. (20+ horses) Basically some are more sensitive than others. We have learned a few tricks over the years though. One method is to tap, tap, tap the neck (or butt) with your knuckle, and then pop them with the shot. It tends to desensitize them to the inital poke. Some horses, you have to tap, tap, tap, 8-10 times (the more sensitive ones) and others less. Use your judgement. When the horse is standing quietly to your knuckle tapping, go ahead and give them the shot. Also, we have a bucket (remember we do 20+) of alfalfa cubes to give them when it's all over. That way, they have something good to remember after it's all over.
A friend of mine does the tapping trick, but instead of the syringe and needle, she just pops them with the needle alone. That way if they flinch, the needle stays where it is. After the horse "calms down" you can screw the syringe on and push the plunger and give the shot. I've never done it that way myself, seems a bit tricky to screw the syringe on, but it may work for you.
We use the alfalfa treat trick also with worming. They tend to not spit the wormer out if they are busy chewing on an alfalfa cube and they think of it as getting a treat. Just squirt into mouth and immediately pop a cube in after. (using 2 people helps the process) Good luck!!