My right wrist got hit with a field hockey ball. i went to the ed, my wrist was fully moveable without any pain so the doctor said no need for an x-ray and it wont be fractured. but there is a lot of swelling, so can it be fractured?

There are many bones in the wrist, and it is indeed possible that a small bone was cracked or broken. Suggest you see a hand specialist, as injury to wrist structures can lead to chronic problems if not addressed in a timely fashion. The copious swelling is a clue that all is not well.

Sometimes, a fracture may not be visible on initial xray, or sometimes evidence of the fracture is only detected when an xray later down the line shows evidence of healing. An MRI can pick up fractures that are not easily visible. Continued pain and swelling would be reason to have another evaluation.