You definitely need to take Crystal to an Avian Vet to have her checked out. Feather destructive behavior that also includes mutilating the body and causing wounds is typically both a medical and behavioral issue. Do not try home remedies on her. Cockatoos are a powder down bird, and using something topical can damage her feathers and powder or be toxic to her. She needs to be seen by a Vet for bloodwork and to have the wound cleaned and tested, The Vet may also do a skin biopsy. She most likely has some type of skin infection. She could have internal or external parasites because she lived outdoors.
As for the behavior aspect, this is a bird who lived outside and has been moved indoors. She had a small barren cage, and now she has a huge cage filled with toys. While these are upgrades, all she knows is her life was turned upside down over night. You say everything scares her, so moving, getting a big cage and then a lot of toys are all very scary. If she is playing with the toys, then that is great. But if she isn’t touching them, then they are part of the problem. Take all but one toy out of the cage, and hang that toy on the side of the cage, below her eye level. She has all these scary things dangling above her. She is a prey animal, so anything coming from above her could be a predator trying to catch her. Put the cage where it is not close to a door or a hallway. She needs to see you approaching before you reach her cage. To have someone suddenly show up from a hallway or through a door is another scary thing. The back of her cage should be against a wall – not close enough for her to chew it but enough so nothing can get behind her. Ideally the cage could be in a corner. If you don’t have a corner, then cover part of her cage, so if she wants to hide, she can. It might be best for her not to be where she can look out a window, because people and pets and wild birds outside can be scary. Look at everything through her eyes, and remove anything scary. Give her time to get settled in and to understand this is her new, better life.
She needs both the Vet visit and the attention to her behavior in order to heal. Getting her treated will make her feel better, and when she feels better, she will be more secure and open to new things.
Thank you for asking Lafeber,