Often what happens with an egg obstruction is that it passes without notice after calcium is administered. The "proof " is behavior returning to normal.
Don't hesitate to pop a calcium tablet into the beak of any hen who presents with those symptoms again. It's not necessary to dissolve or...
Regular calcium supplements given in the water or egg shells are not high enough in calcium to be of much help in an egg crisis. You need something over 500 or 600mg and calcium citrate is the fastest acting.
It's not always a whole intact egg that gets stuck, especially winding down to fall...
Yes, she's very sick. But we can't tell you why. I can tell you that she likely has an infection, though only what might be causing it. The yellow poop can point to a reproductive infection (egg yolk peritonitis) or possible liver failure. Do you detect any swelling in her abdomen? Liver disease...