Holding them upside down doesn't really annoy them that much. A chicken will flap once or twice then generally they relax. (I have had to tip my roo a couple of times cause he used to be a brat!)
Holding them upside down doesnt "hurt them" It scares them. Once they realise they are not hurt, and that there is nothing they can do about it....they stop flapping. After she "throws up" she will shake her head a few times, so be prepared to wear it. AND, IF its sour crop....be prepared to STINK!!! Essentially...its food that has been in there for a while, and not passed, so it rotted. Once you get it out, make sure you get some yogurt in her maybe mixed with some crumbles. The yogurt will help fight off any bad stuff left in there. Good luck with her...