Welcome to BYC. I hope we are able to help you with your hen, and that she will get better. If you haven't posted in the medical/emergencies forum yet, that is the best place to go.
Welcome to Backyard Chickens, Rachel! We are glad you joined the flock! BYC is a helpful site providing all of the information you need to know about poultry. There is always space for members on the BYC roost! It sounds like vent gleet or a severe case of pasty butt. It might be having a bad affect on the egg passing out of the vent as well. Submerge her bottom in warm water with Epsom salts for at least 10-30 minutes gently rubbing the abdomen just in case she happens to be egg bound.