I would soak her in a warm epsom salts bath, this can help reduce some of the swelling. A prolapse will usually not stay in until the swelling has gone down, this is why you need to keep the exposed tissue moist with your hemorrhoid cream. I would wait a while before attempting to push the prolapse back in.
If she is laying down with her head tucked in the corner, she is not doing too well, imho. She is likely exhausted and in pain.
Both males and females can have a prolapsed vent. With a chick this young, it's likely due to constipation/dehydration or it could be a genetic/developmental disorder.
