Natali--I didn't know if you might now of a sedative that would either put her to sleep or at least ease her suffering, & that's why I asked about if you had useful sedatives. I don't know sedatives very much myself.
I would also recommend putting her down manually at this point. To do a euthanization, a friend of mine puts an ill chicken in a bag with a paper bag over its head, and then uses tree branch loppers to sever the neck. That way she doesn't have to see the bird after it is dead. If you have some good strong loppers, I'd recommend that.
You can also use an axe but I like the idea of loppers better.