Some children are afraid of the toilet when they are first learning. It can be a scary thing. Potty training is one of the hardest things we ever learn in our lives. Have you tried feeding her raisins, or prunes, or other fruit to help soften her stool? Sometimes that helps. Offer a book while she is sitting on the potty, or something else that might take her mind off of it.
Have you tried rewarding her when she does go? This may help her see that it's okay. When you see her trying to hold it you might want to take her to the potty and help her relax so she can go. My son went through something similar, he even would not want to eat because he knew it would make him have to go the bathroom. He eventually grew out of this. She may not be constipated, but if her pooh is large it make be causing her discomfort.