Could be a sign of calcium deficiency as well as infection. It's good that she pushed out the egg.
I would suggest giving her calcium for at least 5 days. If you have powder, a quarter of a tea spoon divided twice per day should do it (so 1/8 twice per day). You can dilute it in some water and mash it with your finger until it dissolves. Have someone else hold her, pinch the beak gently with your hand until she opens it and pour the liquid slowly. If you have calcium tablets give her one per day (you can also break it in two and give twice per day to even it out). It will help with expelling egg debris and form proper shells.
I would also suggest whatever broad spectrum antibiotic you have on hand. You can give it to her twice per day alongside the calcium. Dosage varies depending on the drugs you got. It will fight off any infection caused by leftover material until she expels it. If an infection is the cause in the first place, it gets more complicated, but an antibiotic would still help.
I had a hen that started laying rubber eggs with a final one without a shel last month. Started her on the above regiment and she immediately perked up. Started laying normal eggs after 3 days. It's my go to combo for egg/reproductive system issues. It usually works great unless it's something notoriously hard to treat like a salpingitis infection.