this has happened to my daughter about 8 times now. She is about to turn 3 in a few months, and I'm sure it will happen a few more times before she reaches that magic age of 5.
Asyou can see by the comments, MOST of the time, the childe begins to use the arm with 15-30 minutes of being fixed. With my daughter it is immediately, probably b/c it happens to often to her, she now knows that it's "all better" once we pop it back in. But, the exception is that it may take the child MUCH longer to trust that they can use the arm again.
It might help to move her arm for her, and if she doesn't respond in pain, she might be scared that it will hurt, then I would just let her go. Showing her that she can move her arm without it hurting might help or it might not. Children can be sensitive and stubborn and we all have our own personalities. But I would say, as long as there are absolutely no signs of pain, just give her extra time to get over it.
AND I would invest in learning how to reset it as well. We've even had to teach our sitter how to do it b/c she got it twice while I was at work. Although, mnost of the time it happens b/c she has 4 older brothers and acts like a boy with them herself. There's nothing to stop your heart like seeing your toddler rolling around in a pile of 6-16 year old boys.