You can try a warm, mildly soapy bath to relax her, then keeping her alone in a darkened place for rest. You can try lubricating the egg (as best you can) with most anything slippery like vegetable oil, Vaseline, Preparation H, etc. I'm afraid the prognosis is probably not good, though. You might be tempted to break the egg, but there is certainly a risk the broken shell will cut her. This is one time a vet might be able to resolve the issue surgically and have the chicken survive, though she may not lay afterward.
I hope you have been able to help your girl or at least been keeping the membrane moist. I had this happen with a first time layer and with no avian vets nearby, I had to make a decision. I sterilized a razor blade and made a inch long incision. I carefully broke and extracted all of the shell pieces, flushed the area with peroxide, lubricated and carefully pushed everything back in. I also put her on an antibiotic for a couple of weeks to ward off infection. She is doing fine 3 yrs later. Hope everything works out for you.