J.F.
I am a nurse, so I will tell you how we do it for children. (I do not have a diabetic child)
You need to have one room in the house that is designated the "shot room". Every time she needs a shot, take her to the same room (same place). Right now, the only thing she understands is that you are hurting her, and she doesn't know why. As you begin to take her to the same location each time she needs a shot, she will begin to feel safe in her environment & with you, as she will know that the shots only happen in one place, so if she is anywhere else in the house, she is "safe" so to speak. Never give her a shot in her "safe" place, which is everywhere except that one room/ or location.
Step 2, get her involved in the actual administration of the shot ... very slow steps here. (Do this in the shot room)
When you put the needle in, let her push the syringe down. Take it slow, and do not force her. Talk about it to her way before you attempt to do it with her. Practice on a doll first, you put the needle in the doll leg and then let her push the syringe down, make it into a fun game type thing. (this will not be easy and will take time, so be patient with her, and back off if she is not ready).
The more involved she gets with giving herself shots, the more control she will feel she has over this experience and the better it will get for both of you.
(Ask your doctor about insulin pumps)
Hope this helps