If you really want to be sure I would say check with your doctor. That being said.. I think it sounds like an over use issue. This is the time of year where a lot of girls are done with their comp season and working new skills. All sorts of new pains start up....
It is very important that she keep up with her conditioning. Does she do any weight lifts for wrists? That will keep the muscles strong, which will help prevent sprains and other injuries.
As far as wrist supports go, I believe there is a time when they are useful. Our coach asks (not requires) that girls start to use a support when doing Yurchenko vaults. The repetative pounding can start to damage the smaller joints.
My DD had a wrist sprain last year. She was working BHS BHS on beam. over and over and over again.. after she had pain, she was on restriction for a couple weeks (traumatic for her), when she came back she was really tentative on beam. She was afraid of getting hurt again. It took her a while to get back to doing one handpring, much less two. As a matter of fact she went through a couple month period where she didnt do any. After having the skill for a year and a half she lost it. She now uses tape on beam (she uses tiger paws on Floor and vault). Just this little bit of reassurance is all she seems to need to be able to 'go for it' like you said.
Do I like the fact that she feels like she needs tape? No, But her coach isnt too concerned. DD also knows that she needs to keep up with conditioning and the weights.
Hope that helps!
Good Luck!