If you even suspect that your hen (female bird) is egg-bound, getting her to a doctor who is experienced with birds, preferably an avian specialist, is necessary right now. You cannot delay!

In the meantime, making sure she gets some plain water with an eyedropper just inside the beak, a drop or two at a time (slowly, not forcefully) may be helpful in keeping the bird alive until medical intervention.

You can try swabbing her vent area with a bit of KY jelly or other lubricant (not Vaseline) - even regular cooking oil is ok in a pinch.

Set her in a shallow pan of warm water (not hot) - this might relax the muscles enough to pass the egg.

You don't have much time - find an urgent care facility and go now. It's better to be on your way and driving for two hours than doing nothing and losing your companion, right?

She may not only face a life threatening situation here, but this is a common cause of paralyzation in birds. Sometimes permanent.

Egg binding may have any one of a number of underlying causes, including hyperthermia or hypothermia (too hot; too cold). By improving the temperature and humidity in the environment, it could help with the passing of the egg; other causes are malformed egg, poor muscle tone or other health and condition problems in the hen.

There are various methods of treatment that an avian specialist or experienced vet may attempt, but none of these procedures can be executed by someone who isn't highly experienced with the condition; even many breeders would prefer medical intervention rather than chance the loss of the life of their bird. http://www.tailfeathersnetwork.com/birdinformation/egglaying.php

Good luck and God bless,