parakeet swollen vent

My name is Lisa my parakeet has this garbonzo size swelling between her vent and her tail. It droops down hanging below her vent. It is not hard but mushy like liquid is in it. It is dark at the bottom which looks like feces could be in it.

The Avian vet has no idea what is wrong with her. I have had her to see two avian vets. Please give advice. She has lost a lot of weight and her breast bone is very sharp. I have her in a hospital cage and on a heating pad keeping her very warm. She has started eating again but very little. I have been giving her guardian Angel and eggsite bird seed. Spirit is the birds name. She started chronic egg laying at four months of age. However, she has not laid an egg in about one year. She is two years and four months old. I love her very much. Please Help!!

Thank you, Lisa