Why not? Worked for these two.
There is a way for you to experience what your DD's pitching arm is going through. Stand up and do a windmill motion with your arm as fast as you can for 5-6 revolutions. You'll feel a tingle in tips of your fingers from the blood being forced there through centrifugal force. You heart can not overcome the force and the blood stays in the hand. Once you stop the heart removes the excessive blood. Your DD is doing way more than that each game. So long as the swelling goes down and she feels no numbness or pain she should be good to go. If the condition persists for a long time after she's done pitching then have her checked out.
Kinzie Fowler, formerly an AU pitcher has Thoracic Outlet Syndrome. Her hand would swell badly. She had a rib removed to try and alleviate the condition.
http://www.azdesertswarm.com/other-sports/2014/5/8/5693942/arizona-wildcats-softball-kenzie-fowler-injuries-career
My DD has this, too. Couple of things...
Lastly... this condition... any condition... should have some sort of preventative/rehabilative routine associated with it. As the cause is usually circulation THROUGH the chest, lengthening stretches of the chest (not that stupid all too common posterior stretch)... should be a part of your regular routine. In addition, shortening of the rhomboids like band scap routines NEED to be a regular part of a routine.