I agree with the others, sounds like a ruptured air sac. Can you post pictures of the wounds?
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Thanks for the video. Gives a good idea of were I need to really examine again.Here is a video showing the avian respiratory system so you can see where the air sacs are located. When an air sac is punctured or ruptured by injury the air leaks into the body under the skin causing the swelling. Small tears or punctures may heal on their own, but pressure from built up air can keep that from happening. If bacteria gets into the air sac then antibiotics may need to be given. If the air continues to accumulate then I would release it as needed.
https://www.centerforanimalrehab.org/first-aid-and-your-pet-bird/
I will search her again tonight and try to find something I obviously missed. If I find something ill be sure to take some photos.I agree with the others, sounds like a ruptured air sac. Can you post pictures of the wounds?