I'm sorry about your pullet
I have not had a prolapse with an egg, but do have a couple of videos to link you to. A few folks have been able to get the egg out after watching them - it may be worth a shot. (both videos are by the same girl, the second one is an update, the hen survived and is doing well)
As for culling, that would be up to you - you are supported whatever decision you make. A prolapse by itself can sometimes be hard to fix. I have ended up culling a pullet with a severely damaged prolapse. Right now, your girl's tissue looks "healthy". Keeping it moist will be important - use what you have on hand - honey, coconut oil, Prep H, etc.
If you want to work on her and see if you can resolve it, I suggest you take a deep breath, gather all your thoughts and supplies, have them at hand and then proceed. Hope for the best, but prepare yourself for the worst. I wish I could offer more - please keep us posted.