No lice removal products are 100% effective when it comes to killing the eggs. You still need to sift through the hair with a fine-tooth nit comb (you can buy one at your local drugstore) section by section and remove any nit you find by hand.
Be aware that not all lice shampoos are safe for young kids. Permethrin is approved for use in kids two months old and up, and ivermectin (Sklice) is approved for kids six months and up. However, if your child is two years old or younger, removing nits from the hair is the safest first line treatment to stop a lice infestation.