Do nit combs get rid of nits?

No, the combs remove the adult head lice but not the "nits" which are their eggs, which they stick to the base of the hairs.
So if you have nits, coming out the adult lice will not remove the infestation as more lice will hatch out from the nits.
As well as combing the hair you need to kill the nits with some proprietary medicine.