If you really REALLY want to save this chicken taking her to the vet might be your last resort. I'm sure the could do a quick surgery and take it out and she could make a quick recovery.
That is exactly what I was about to recommend. It might be a little painful for her, but if you can squeeze her crop with your fingers to try and locate the screw. When you do keep squeezing under it and literally push it up her throat! If my birds eat something I make them drink a lot of water...