UPDATE:
Ok, so, she has been doing fabulously well. Her vent has stayed in since the last time I posted about it. She has been treated like royalty, inside next to a heater. She's been having food, coconut oil, and scrambled eggs (which she is CRAZY about!). We had had her in a dark room so that that she could heal for a while without laying eggs (though we've been taking her out frequently in short increments so she can still be a chicken). I think the respiratory problem (her nose being stuffy) was from the heat change- from being in a barn to being inside with the heat on.
We just moved her outside to the barn yesterday. We put her in a crate, but where she can still hear the other chickens and stuff.
So today she laid her first egg (which we were still kind of trying to prevent... but I guess it needed to come out). It had a very, very soft shell. So much so that the first part of the shell came out, with the yolk and whites and stuff. And then she was still pushing like she was going to lay another egg, and she laid another piece of soft shell. I found her in there eating it, so I went in and took it out. She's not straining anymore, so I think she got the whole egg out. Her butt still looks good, and everything like that seems good.
But does anyone know why the shell would be soft like that? She's on layer feed. Is it because her "system" is just getting started up again? Is this likely to be the case again tomorrow? She is not acting like she's in any pain, seems completely normal after getting that egg out.