Change4good you did well. I taught for 25 years and I can assure you that lice aren't fussy about the hair they reside in, this is not an indicator of not been sufficiently clean.
You don't mention your daughter's age but she or you should check her hair twice a day. If her hair is long I suggest plaiting (braiding) it and pinning the plaits against her head each day for the duration of the lice infestation.