Continuing to comb out and pick nits is as important as the initial treatment, don't let it go even a day longer and risk that any nits will hatch and start the infestation all over again..
This. I never heard of any device that can kill the eggs. You have to remove them. OP, I know the laundry is time consuming, but when dealing with lice, it's all you do. Order pizza, forget about cleaning. Just comb.
Ironically, dd had just sprayed her hair with Fairy Tales lice repellent before I checked her - my girls use it daily.