If her abdomen is swollen, then my guess would be ascites or internal laying rather than egg bound....especially since you can't feel anything internally. One egg stuck in the system is not likely to make a really noticeable swelling or bloating of the abdomen.
If it is ascites, then draining it will give her relief but fluid will most likely build up again and need to be drained at infrequent intervals. If it is internal laying then she may be ok for a few weeks or months but sooner or later an infection will set in and she will start to look very sick. Antibiotics can help with the infection (peritonitis) at that stage when she is acting sick but it will be a recurring problem as there is no treatment to prevent the internal laying although I believe it will get to the stage that it is self limiting....no more room.
Obviously, carrying excess weight around in her belly like that will make it more difficult for her to walk (she may start walking like a penguin as it pushes her hips apart) and put a strain on her organs. I think the best you can do is make her life as comfortable as possible and be prepared to euthanize when her quality of life becomes poor. You may be lucky and she survives for a year or more or she may deteriorate quite quickly.
I can't afford to take sick chickens to the vets, especially when there is a likelihood that they have something potentially terminal that there is no treatment for like Marek's or internal laying. I give them as much tlc as I can and end their suffering as quickly as I can when there is no hope. That is my philosophy but everyone has different ideas.
If you think it feels like a water balloon (ascites) rather that a hard mass, then you could try draining it and that is about all the treatment I could suggest in this case.
Good luck with her.
Barbara
