Do you have a video of the duck?
How is her appetite, is she eating, and drinking - more than one of the other?
In consideration of the suddenness of the symptoms, I would be inclined to believe the paralysis is related to obturator paralysis, or possibly trauma to her legs or spinal cord. If you haven't already, I would suggest bringing the duck inside and set her in a warm, humidified area.
Once you have her inside, palpate her abdominal area, and not whether it feels hard or distended at all. Diagnosis of an egg in the oviduct can sometimes be achieved by sticking a lubed finger up the duck's cloaca one to two inches. Thoroughly, inspect her legs for swelling, discoloration, or abnormal sounds when the joints are bent.
Maintaining hydration status when an egg is stuck in the oviduct is vitally important. Ensuring that, you can add some electrolytes to her water, such as Sav-A-Chick, or Gatorade. Considering she may have an egg stuck, you may try orally dosing her with some calcium; several supplements can be given - if you have Tums on hand you can crush one up and offer her that, or use calcium gluconate 23% dosing at 0.2ml per pound orally, or give one pill of calcium citrate.
https://www.tractorsupply.com/tsc/product/durvet-calcium-gluconate-500-ml