Sick chicken--Egg bound but had thin shelled egg?

Ok, typing one handed with hen in hand. First chicken "emergency."

Golden Comet, 25-ish weeks old, lethargic this afternoon, hunkered down. Went down at 6:30 to close chickens in. All in but this girl. Hunkered down in the cold with a squishy egg laid under her. Dripping white gooey stuff all over me when I picked her up.

Egg bound? Read to stick in warm water in sink. Had her soak for 10 minutes.
Very tired.
Tried to get her to eat Smushed Tums. Wouldn't eat.

Took out of tub. Wrapped in towel. 20 minutes later she struggles a bit and I stand up with her. She drops 2nd totally squishy egg on floor with me holding her.

Is she out of the woods since she's passed 2 eggs just now? Will carefully blow dry her. Have her in dog crate inside for the night.

Chickens have free access to feed, oyster shell, and grit. Small amounts of Scratch in am and PM.

What else should I be doing or watching for please?
Thanks!
SArah.

 

The above pics are the two eggs she passed in the past two hours. Think this is a good sign? What else can I do for her?

 

She seems fine today! Added Tums to some mash for her last night and today, and she's wolfed it down. She's all dry and fluffy after a night inside in a dog crate, so I'll put her down with the others in a bit.
Guess I'll have to mix some oyster shell in with their actual food--I have it out 24/7 in a hopper next to the grit and feed, but I wonder if this girl isn't eating it. I have one chicken that lays eggs with thin, scratchy, sandpaper shells. Maybe it's her?!?