I too had a hen that filled up like a water balloon. I have a thread on here about it. She kept getting larger over the course of about a month but was laying eggs until the last week or so when I finally knew I had to try something. She was so swollen she could no longer walk - she was just a huge ball - and her skin was splitting open for being so swollen. I could tell it was a water balloon feeling so knowing I had nothing to lose because I was going to put her down - I first sat her in a warm Epsom bath soak, gloved up, and probed her vent. I had to reach way up but it was easy with her being in the water and she didn't seem to mind. I did find an egg and had to break it to get it out. Again, much easier with her soaking in water. It continued leaking out of her for a day so next day I repeated the procedure and got the rest of the shell out that I couldn't find the day before.
Next issue was the fact that she was so swollen with water. I used a hyperdermic needle/syringe and literally drained her. I inserted the needle in the watery balloon area to the left and right of her vent where I could push in and feel there was nothing but fluid there. Unfortunately the only syringe I had was very small so I had to stick her repeatedly but I draw out over a cup of water. Water continued leaking out of her for an hour or so from some of the holes her skin was so stretched. I placed her on folded towels and she soaked through three - I mean soaked. I could pick up the first one and wring it out. I gave her Penicillin shots for a week. The water swelling went down the next day and by two days later she was acting and looking like her old self. Today, three weeks later she is doing great and I can't tell which one she is. I think she is laying again but can't swear to it. I have seen her in the nest and I'm getting large brown eggs again.
Take a look at my thread or PM me if you need more info. If I had it to do over again I would get the smallest needle I could (which I did) but I would get the largest syringe so that you can draw out more water without having to restick. They sell the needles/syringes for pennies at the feed store.
Hope this helps - at this point, like I, you have nothing to lose by trying.