I'm no expert in the anatomy of the louse, but I'd guess that yes, there would be something that makes it continue itching after the bite. (Isn't that just true of all bloodsucking insects?) Also, the chemical treatment might be causing you to itch for several days afterward.
Following the chemical treatment, heavy oiling should work in suffocating the rest of them (if there are any). Look up their life cycle; oiling doesn't suffocate the eggs, so that should give you an indication of how long you'd need to continue for.