This condition is known as Pharyngeal Diverticulosis(Zenker's Diverticulum) wherein your daughter's throat has developed a defect creating a pouch which lies between the throat skin and constrictor muscle. This is commonly seen in musicians using wind instruments like clarinet and saxophone players who generate tremendous air pressures in mouth and throat when they play these instruments which exposes any anatomical defects in the constrictor muscle to push through the defect causing this diverticulum. She will require pharyngeal surgery to correct this condition.