Snow White, I would bring this up with the school, if you haven’t already. If your daughter keeps getting reinfected it’s either because you aren’t getting all the eggs out (itching just thinking about it) or that another child in the class isn’t being treated for nits properly!
As for treatment I found the best treatment was any nit shampoo, then plenty of conditioner and nit combing EVERY night for a week or two! We used the Nitty gritty comb which pulls out eggs too! Then use a shampoo with tea tree oil, as apparently Nits don’t like it! No idea if that’s true but I always used a shampoo with this in and I NEVER got nits even though I was in contact with the 3 children I looked after and all 3 had them at one point!! Nightmare!
Good Luck, hope you are all nit free soon!