Nobody likes to get shots. Trying to minimize the pain of the injection and reducing the anxiety of getting one is well worth the effort.
Do Not Get Anxious yourself, your child will pick up this vibe so fast your head will spin.
Distract Distract Distract by doing anything that works, sing a song, tell a story, have your child focus on you and your face and keep them entertained while the medical staff goes about the injection business. If there is a Child Life Department at your hospital, they can help and certainly can teach you how to do this.
There are products such as Buzzy that work by providing a vibration to the skin that detracts from the pain of any shot. Kits are available that include distraction cards to help kids keep their minds away from an incoming shot.
You can try an ice cube but I wonder if the whole routine of getting an ice cube and numbing the skin will just add to the anxiety level., but it might help with the pain of it. There are also numbing gels to try that give the same effect.
Hopefully you and your child wont have to get too many injections, I dont know if it will ever get to be easy for anyone.