Well done Speckybat, hope your buffered/buggered up eyesight is better. 
It is very possible to clear an infestation by effective combing over a period of time. Doing a throrough comb with conditioner 2-3 times a week for as long as it takes. The eggs are laid on and glued to hairs next to the scalp so are difficult to catch in the nit comb until the hair has grown a little way off the scalp. Because it only takes 7-10 days for the eggs to hatch, and similar for the females to mate and start laying more eggs, combing needs to continue for around a month minimum to get all the eggs and the little live b*ggers, otherwise the cycle just continues.
So it's possible to clear lice without chemicals if you have the time, the patience and a compliant Dc. If you have lots of Dc's who hate having their hair combed, then you're on a hiding to nothing.........
The irritation is not the lice biting but the lice poo causing a sensitivity, and can continue for a while after all the lice have gone. So don't assume the treatment has failed if your Dc is still scratching - look for live lice.
The empty shiny nit cases can persist after treatment until combed out, but only treat if you find live lice.
A few very important points for successful irradiation if using chemicals:
Read the instructions carefully in regard to the length of time the stuff needs to in contact with the scalp, it varies dependant on the product used.
2 treatment a week apart are usually required.
Make sure you have sufficient amount for each treatment, don't skimp.
Don't go swimming in chlorinated swimming pool for a couple of days either side of each treatment and make sure the hair has been washed between the last swimming session and using the treatment. Chlorine can affect the efficacy of some preparations.
If you have been using conditioner after shampooing or for nit combing, then wash hair before using the treatment because conditioner makes the hair 'slippy' (especially the silicone based ones) and can act as a barrier coating between the hair/eggs and the treatment product.
Don't use on water wetted hair unless the instructions specifically say to, as this can dilute the chemical.
Sorry for such a long post, but be grateful it isn't a PP slide set with close-ups!