Misshapen eggs and swollen bottom

[thesechickens]

I have a speckled sussex that is 9 months old. I noticed she had a swollen bottom a couple weeks ago. It feels soft and when I press lightly on it she doesn't seem to mind. She still lays eggs but they are misshaped, as if they were being squished while they were being formed. She is acting normal, still eats, runs around (though with a bit of a waddle), and picks on the lower ranking chicken(s). I've given her a warm bath, put providone iodine on her, and put neosporn because there was an open sore on the raw butt. After the bath she looked better than before the bath but I think that was only because the feather weren't crushed with poop. It's hard to get a decent picture of her bottom without someone else's help but I tried.
I wondering a few things. First, what can I do to help her without taking her to a vet? Second, is it safe to eat her eggs? Third, could there be something wrong with her that would make it unsafe to eat her?