I think it could hurt if it was cold going in and depending on the location of the needle stick. I am sure they could let it get to room temp first, they may need it cold for storage purposes, but its not going to go bad if they just warm it up in their hands first.
Another reason it may hurt is the size of the needle, if they used a bigger gauge this time, it could hurt.
So sorry Brandy had to hurt for this, It is so hard when they cry
I gave my Bichon shots (diabetic) for a long time, and kept the insulin in the fridge, I always rolled the storage jar
in my palms for a couple minutes to warm it up before I gave him the shot. My vet showed me that.