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Something similar happened to me last fall with my hen Philo. She had a head wound down to the skull. My suggestion (from painful experience) would be to not cover the wound in any bandage or cream. With Philo, I covered the wound in antibiotic cream given to me by the vet and the next day she had an enormous infection. The bacteria festered beneath the antibiotic ointment and infection grew between her flesh and her skull. For a month I had to lift the skin off her skull three times a day every day and clean it with a Q-tip until the wound healed. The entire time she had to be in isolation so the other birds wouldn't pick at her wound. She healed, though, and is now a doing very well with only a slight scar to show the trauma she went through.
With Eve, I couldn't tell from the picture if the wound reached the skull. The deeper it is, the higher your chances of infection if it's covered. Leave it open, and use an antibiotic spray. If her skin is ripping, I'd recommend going to a vet to suture it up, but otherwise you'll have to make do and hope it heals on its own.
I hope she gets better!