I'm afraid that looks like internal laying rather than egg bound. An egg that is stuck in the oviduct or cloaca will very rapidly make the chicken sick because it blocks the passage of faeces. Also an egg that is stuck through egg binding is higher up in the body. It cannot be down between the legs like that. A couple of days with egg binding and she would be looking really ill. This has almost certainly been going on longer than two weeks for that amount of swelling. The fact that her comb is nice and red suggests that she is still ovulating, but the eggs are almost certainly dropping into her abdominal cavity instead of passing into the oviduct when they are released from the ovary. It is a common ailment in chickens and sadly not really curable. The yolks released from the ovary fall into the abdominal cavity and settle in the bottom below the intestines. Over time a large mass of them builds up and starts to put pressure on the internal organs, like the heart, lungs and intestines, which become constricted and poop becomes watery because the solids struggle to pass the constriction. The bird will usually have soiled feathers below her vent as the poop can no longer fall clear because of the swelling and the birds legs will get pushed wider apart by the mass between them causing a penguin like stance. Often some of the fluid leaches out of the yolks and puddles in the bottom of the cavity and the yolks solidify and float on top of it. Draining the fluid (which is referred to as ascites or water belly) can give almost instant relief, but unfortunately it will build up again and need re-draining at regular intervals. Eventually the mass of egg yolks will either cause organ failure or become infected (Egg Yolk Peritonitis) and the bird will die.
Some people are reporting a big improvement in birds that are given a hormonal implant to prevent ovulation, thereby preventing the situation from getting any worse, but it is expensive and needs to be repeated every 3-6 months.
You can try draining her yourself or take her to a vet. There are You Tube videos that show you how to do it and whilst I understand the thought of sticking a large needle into your chicken is scary, she will almost certainly die in a few weeks or months if you don't. That said, if she is approaching her first moult, she might naturally stop laying and improve over the winter, but the problem will reoccur in the spring when she starts to ovulate again. The weight of the mass of yolks will have pulled her system out of alignment so that there is little chance of her ever laying normally again.
I'm sorry it is not good news for her or something that is easily fixed. Draining her should buy her some time whilst you research your options.
Regards
Barbara
