I'm definitely not an expert at this, but I think the fact that she had a big poop is a good sign. That means her digestive tract isn't blocked. I have a hen who acts egg bound on occasion, but it's never been a hard shelled egg so she eventually just kind of poops out raw egg. She'll act sick for about a day and then she poops it out on her own and she's fine. Scares the heck out of me every time though. If it is a soft egg I think it might actually help to break it so it's easier for her to expel. I've done that a couple of times with my girl and it seems to have worked out, but sometimes I just leave her and she takes care of it herself. It's hard to not do anything when you know they're not feeling well, but it's happened enough times with her that I'm getting more comfortable with it. It's never lasted more than a day with her though, so I would intervene if it went on longer than that. Did the poop look like it had egg in it?
If somebody else with more expertise is reading this please chime in if this isn't the best advice!