Having been that toddler.....
Couple possibilities here
1) This is the FIRST time, it was traumatic to you, it was traumatic for her.
The second time, the fifth, the hundredth it will not be scary/traumatic for anyone
Unfair, yes. Traumatic, not unless you let it
2) Make 10,000% certain the insulin pen/vial is NOT cold. Injecting cold insulin hurts
Roll the vial/pen between you hands like you would clay, and were trying to make a long thin piece of it from a larger ball.....
3) Having done shots since I was your daughters age, almost certain it upset you and slowed you down. Whole thing shouldn't take more than 30 seconds IF, if that long beginning to end.
If it is taking longer, consider that "build-up" increases HER discomfort because she senses your anxiety.
Pull it out,
dial it up
pick an injection site
get a handful of her skin
leave needle in for a couple seconds
pull it out
On with the day
all the normal
You could look for a smaller gauge needle whether its a syringe, or the pen tip.
I've always found the smaller length/thickness silly.... and becomes counter productive at some point. In plain English truly does not matter how skinny the needle, how short the needle might be,
IT IS STILL A NEEDLE, period.
Never mattered to me, size, thickness, it was needle, and necessary
4) Have you ever injected yourself, NOT WITH INSULIN... but simply putting a clean, brand new tip/needle into your own leg, for example? You do it, your partner does it.... it time your daughter will do it all by herself with insulin. You'll always watch her do it until she becomes a teen)(, but in the future she will.
6) There are couple target spots, less ouchy usually.
Butt is easiest, and she wont see it coming, just gold her still for a second, and ALL DONE lets grab that toast.
Happy to explain, if needed