IF there's a shell, and it's likely there is as you didn't see yolk, you will want it out of there.
You can use a method that is used to remove eggs in chickens. It's a little gross, but this is a life-saver method.
Put on gloves. Oil your pointing finger with olive oil or mineral oil, etc. Gently insert it into the top of the vent of the bird to feel for the shell. (If it were an egg, you'd go above the egg with your finger and use your hand on the abdomen below to gently locate the egg and draw it back to the vent).
If you find egg shell (or even if you do not) you will want to flush out her vent. Some say olive oil, and that treatment seems to work well and is safe. This is quite similar to Glenda's method which is based on textbooks on poultry keeping as well as years and years of experience.
For the broken shell method of removing eggs (mostly recommended for oversized eggs), my text suggests that after the egg is broken, flushing the interior out with cool (not cold) antiseptic treated water to flush out the egg shell bits and the yolk/white, and cool the area from inflammation, and treat in case the shell cut any of the interior.
When this is done, we need to address the "why's" of the egg.
If you're not doing it already, I would suggest that you immediately feed as follows:
Laying mash as 95% of the diet - free choice.
Oyster shell - free choice, separate from the feed but next to it.
Granite grit - free choice - mixed with the oyster shell.
Yogurt (plain unflavored) daily for the next 5 days (1 tablespoon)
Possibly: crush 1/2 tums tablet and mix that in a quickly eaten damp mash for her, or scrambled eggs. Do this once only. Do the other things daily.
Then I'd be on the lookout for infection. Penicillin is an appropriate antibiotic for an issue like this. (Terramycin not so much.) The best bet, of course, would be to notify a vet that she broke an egg in and could you pick up a good antibiotic like Baytril. If your vet won't dispense, then watch her. At any sign of lethargy let the board know.