Hi,
Eggs probably is not the cause of hiccups.The stomach or intestines when distended irritates the diaphragm (this is a curtain between the abdomen and chest) and hence hiccups are generated.Her
constipation needs to be tackled give high fibre diet like green leafy vegetable and fruits .You can try giving her sweets like sugar to reduce her hiccups.If it continues for many hours without relief then let her docter examine her who might suggest some medications.
Bye
Take Care