Have you felt inside her vent?
Sometimes just doing that will open up enough to let her expel what's in there.
No first aid supplies on hand at all?
If tissue is getting exposed, you can apply a bit of vaseline or honey.
The only way to feel inside the vent is to feel inside about 1-2" if you feel something hard, there's an egg. If it's a soft shelled egg, then you may not feel that.
Looks like she's leaking poop(?).
Have you seen her poop?
How is she doing?
I would separate her since she's getting picked at. She may also be picking at herself too.
You may need to feel inside the vent for an egg.
Looking at your most recent photo with the blood, her struggling to poop, etc. I would say she may be trying to pass lash material...