Wait and ask the vet for an antibiotic. Amoxicillin is a common one we use on chickens. The vet may have another one in mind after he examines the hen.
Thank you for such a thorough narrative! Well done and so helpful!
I'm going to guess she has an infection. It may be a general bacterial since I see no egg tinged color to the poop, but the poop does appear to be indicative of infection.
Do you happen to have an antibiotic on hand? It should...