If you poked her on her lowest point on the right side of her abdomen and got egg yolk material, she has a very advanced case of internal laying and egg yolk peritonitis. You did not make it worse or puncture an egg in the process of laying, you just got more information by figuring out that her abdominal cavity is unfortunately full of this material from her internal laying issue.
Her hormones have kept her "laying" but the egg material has just been dumping into her abdominal cavity. Chickens do not have a diaphram that separates their organs, it's just one big cavity.
I've had just one case like you're describing. That one I used a syringe on and removed over 60ccs of disgusting scrambled egg goop from her on multiple occasions - which did help her for a bit. Every other bird I've drained, and there have been many - have been full of fluid.
You can of course try antibiotics, and you can try and get as much material out of her as possible by draining/ The other thing you can try is putting her in a dimly lit area for a few days to help stop the hormones that are continuing to drive egg production to at least put a stop to more material being added. These are all treatment options to help her be more comfortable- none will cure her- and as such it's up to you whether to treat her or ... Draining fluid is one thing - this level of disease is something else.
If you have a strong stomach and would benefit from photos of a necropsy of an EYP type case-- but be warned, it is VERY GRPAHIC so if you will find photos of the inside of a chicken impacted by this disease disturbing - DO NOT CLICK ON IT.
https://www.sufficientself.com/thre...-they-stop-laying-warning-graphic-pics.15366/
