You also asked about lime juice,it does not have any proved effects but being an antioxidant like any other antioxidant it will have beneficial effects on sperm count. ...
I dont think Mountain Dew is a choice of fluid for her, as it is carbonated and will make the childs condition even worse. also the carbonated drinks have all kinds of preservatives which can upset her stomach even more. Stick to Oral rehydration Solutions that contain glucose , sodium etc., If shes still throwing up after waking up, you need to take her to a doctor and consider admissions with Intravenous fluids ( as her oral tolerance is poor ), medications for Vomiting, abdominal pain / gastr ...