In any medical emergency, and chickens have them as well as humans, we need to treat shock first before any other thing. Shock from nearly being killed by a predator and now intense pain from the beak injuries add up to life threatening shock. The easiest is to warm some Gator aid and syringe it into her beak very gently. Give a couple ounces every hour or two. Hydration is essential.You can use 81 grain chewable aspirin. Since there's lots of pain involved with beak injuries, I would dissolve it into the Gatoraid. You can give one whole aspirin two or three times a day spaced out.
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Once you treat for shock and the aspirin has taken effect, I would assess her physical state. Try to get her to stand. Assess her strength to stand, her balance, and see if she can manage a couple of steps. If she is unable to accomplish any of these things, as
@aart mentioned, she may have a brain injury. If that's the case, she will not recover.
The puncture wound already is guaranteed to have bacteria multiplying in the tissues. She needs to be on an antibiotic. If you have any left over prescriptions on hand, tell us what it is and what strength and we can help to figure out the dosage.
Trying to fix the injured beak at this early stage is not a priority. Stabilizing her and treating for shock and pain come first.