Hi
Sorry to hear your hen is not well. It sounds like she may be laying internally, but probably not infected yet....which would be EYP. They can go a considerable time laying internally before infection sets in and sometimes the build up of yolks and fluid in their abdomen causes organ failure and they die without getting an infection, so Egg Yolk Peritonitis will not necessarily happen and antibiotics would not help unless there is an infection.
Unfortunately once they have started laying internally, it is unlikely that they will ever manage to lay properly again and your best course of action is to try to prevent them from ovulating, so that the mass of yolks in their abdominal cavity does not increase. This can be done via hormonal implant (superlorin) every 6 months or so which will work out pretty expensive, spaying, as has been suggested by your vet, but that is major surgery for a chicken and also expensive and risky, or you could reduce her exposure to daylight and food and see if you can trick her body into moult and winter "non laying" mode. I don't know if the latter will definitely work but I certainly saw my internal layer improve dramatically over the autumn moult and winter period, only to notably deteriorate in the spring when she started ovulating again. Trying to trigger her to go broody might be another option, if she is a breed that has a tendency to it. Again, a restriction in food and a nest of eggs may help to stimulate it.
It may also help her to be drained if there is a fluid build up (ascites) which often occurs with internal laying. Draining can give significant relief but usually needs to be repeated and will only treat a symptom not the cause.
Good luck with your girl.
Regards
Barbara