Dear Lisa,
No, this is not normal, and requires some intervention. It would help to have your daughter sit on the toilet at school at intervals, regardless of whether or not she says she needs to use the bathroom. Also, it might be useful for you to go in early and help her to become more comfortable with the bathroom at school, so she's not avoiding it. You can also implement a simple reward system, whereby you will give her some treat or other reward each time she uses the toilet at school.
Once you take away the pull-ups, don't retreat from this position. If you do you will only reinforce the behavior you want to extinguish.
Does it hurt when she urinates or defecates? I know when I was little I used to have UTIs all the time and I hated to go to the bathroom. My 5 yr old has very hard stools and it hurts him to defecate. So I started giving him oat bran tablets to help with fiber and now his stools are soft and he no longer dreads going to the bathroom.