I agree, don't release her - see if there are some Falconer clubs near you - they'll take her as a donation and use her for training their falcons to hunt. Dry ice can be purchased at most any grocery store if you decide to go the euthanasia route.

And the cocked head is an inner ear infection. It won't heal on its own and she needs antibiotics for it, but even then, it may not heal if there's already scar tissue.