Another vote for combing and conditioner. Last time I had nits (nearly a decade ago thankfully!) I combed them out with loads conditioner. It's the combing that does it, the conditioner just makes it easier. You have to do it a few times to catch all the newly hatched ones, but it really does work. You don't need to put poison on your head.
There are treatments available now that don't use pesticides that are safe to use. They are the ones that contain silicones such as dimethicone or cyclomethicone (also used in shampoo, conditioner, skin creams etc).
Alternatively, put lots of conditioner on your wet hair and thoroughly comb it with a nit comb. Repeat 2 days later or as often as needed.
Hope you manage to get rid of the little buggers soon
My daughter has had headlice a few times and I can assure you the ONLY method I have used to get rid of the little so-and-sos for the past few years is conditioner on damp hair and 30 mins of combing. It REALLY works provided you comb regularly over a week or so and make sure you wipe the comb on kitchen roll after passing it through the hair each time AND sterilize it when you've finished each session. You do not need to buy any other products.