It sounds that you've made the connection between your neuralgia and the dental work (specifically root canals) - read up on root canals and their dangers (not so much for the actual procedure but the fact that your leaving dead rotting tissue in your body to cope with).
Neuralgia may simply be your body's cry that something is wrong with the dental work, whether there still an infection or simply because the roots of the teeth may be unproperly removed - even if the root canals were done properly neuralgia is a possible symptom of having a dead tooth breeding infection and possibly spreading around the region.
The most sensible approach would be to have the offending teeth removed, however it's not a simple decision - there may be temporary options to mask the problem as you say.