If a bird cannot lay an egg, she is considered Egg Bound. This can be a very serious condition.
It can be due to an infection in her reproductive organs, a soft shelled or misshapen egg, nutritional problems or obesity.
It is also more likely in young birds that have not laid before. But none of that matters when it occurs.
Catch the duck and lubricate the cloaca and egg (if it is exposed) with KY Jelly, being careful not to tear the lip of the cloaca,
and then place her in a warm, moist environment. Try setting her in a pan or pool of warm water for an hour.
If this does not help, try gently massaging the egg out, continuing to lubricate the cloaca.
The last resort, if the egg is exposed, is to put a small hole in the egg and remove all the contents with a syringe.
Then you must break the shell and remove it. Be very careful as the edges of the shell are sharp and can cause lacerations in the oviduct.
If you must perform this operation, then you should put your bird on antibiotics for a week after the operation.
See the recommendations in the
Bumblefoot section on antibiotics and probiotics.