Possible Egg Yolk Peritonitis + Something StRaNgE???

Hello all, my name is Val and I'm pretty new to caring for chickens. Now, normally I'm able to find most, if not all of the answers I need on here or elsewhere online, but I'm at my wits end this time and hope that someone can please help me out. To make a long story short, I found my (almost 2yr old) Rhode Island Red hunched, standing still, and not eating yesterday afternoon, as her crop was nearly empty, so I brought her inside to care for her. I gave her a warm soak that evening, because I thought that she might be egg bound. It seemed to make her feel a little better, but didn't result in anything and she still would not eat, though she Was drinking water.

Moving forward, the next morning while she was still inside, she laid an egg yolk alongside a soft shelled egg, which I'm assuming is what they call "egg yolk peritonitis," But there was something inside of the shell that I have never seen before...what looked like a big chunk of partially cooked meat. I am providing photos, because I am stumped as to what it is, what caused it, and what I can do...if anything, because a vet is out of the question. Once she got this stuff out of her I let her outside and she seemed to be acting more like herself again...bawking/clucking, walking around and eating, pecking, etc.. I checked on her throughout the day and aside from not having her Full appetite (she's normally a little glutton), she's pretty much back to her normal chatty, hyper self, though I'm keeping her inside again, so I can monitor her poo and whatever else comes out of her.

Oh, I should also add that she was laying regularly up until a few weeks ago, which I figured was due to her molting, though she still looks for a place to nest and will sometimes sit in the nesting box for a bit, but does not lay anything (that I know of). The others all molted in a fairly timely manner before her, but she seems to be taking much longer. She is also at the bottom of the pecking order and gets picked on by a few of the others, which makes me want to get her well all the more. *Sigh* I never knew caring chickens could be so complicated. I do have oyster shell available btw, but not all of them will eat it. *Argh* ANY helpful advice, suggestions, etc., would be Very Much appreciated and Thank You all in advance in case I'm not able to respond right away.

P.S. The first photo in the collage is of her poop the night before.