Your hen has Mycoplasma Gallisepticum. It's an infection of the respiratory system that Spreads to the eye. It can go on to inflame the reproductive system and GI tract.
Tylan may not work. Oxytetracycline is specific to respiratory problems, where as Tylan is a broad spectrum antibiotic. If your hen wasn't exhibiting symptoms of wide spread infection, I'd have more confidence in the Tylan. But you're listing off the entire shopping list of major symptoms.
First off, a warm soak in Epsom Salt. If that soft shell wouldn't just slide out AND she's prolapsed, I bet folding money there's more than 1 in there. Some calcium citrate and a warm soak will go a long way to resolve that.
If you don't have Oxytetracycline or can't get it, you can administer the single dose of Tylan in conjunction with 425mg of Baicalin (Chinese Skullcap concentrate) 3 times a day.
Put her in a dark place to prevent her from ovulation until you get this resolved.
Continue warm soaks daily until the prolapse resolves.
I lost 3 hens consecutively with similar symptoms. They all had multiple soft shells backed up. 1 had 17. Make absolutely sure you administer that calcium citrate.
https://www.merckvetmanual.com/poultry/mycoplasmosis/mycoplasma-gallisepticum-infection-in-poultry#:~:text=Treatment, Control, and Prevention of Mycoplasma gallisepticum Infection in Poultry&text=Most strains of M gallisepticum,act on the cell wall.