Here we go. According to my chicken bible, Storey's Guide To Raising Chickens, it does indeed sound like binding. It occurs when a too large egg gets stuck in the vent. This can happen to pullets. You are supposed to dislodge the egg.
You are supposed to put some KY jelly on your fingers of one hand, insert your finger into the vent and use the other hand to push on the abdomen and work the egg toward the vent.
If you can see the egg but you can't get it out, you are supposed to break the egg and remove it carefully, being careful not to damage the tissue with bits of sharp egg shell. Then you rinse away the remaining bits with hydrogen peroxide in a squirt bottle.
If any tissue protrudes, you are supposed to treat that with Prep H and isolate her for a while until she heals. Otherwise, other chickens will pick at her.
So sayeth Storey's