I think that you need to have a 'cocktail' of a pain killer along with your neurontin.
Most of us use something in the opiate, or synthetic opiate class along with neurontin or Lyrica.
I take Tramadol (generic Ultram) @ 100mg 4x day along with my Lyrica, but was taking the same before I switched from neurontin (6+ years on neurontin, plus Tramadol ).
I'm not sure that it can be taken along with Valium (Diazepam) and may knock you loopy, if you do. But the Diazepam is a mild trnquilizer and is used primarily for anxiety (sometimes as a sleep aid), but isn't for pain-usually.
I think that you need a pain killer for that burning.
But 2400 mg of neurontin is just about the base minimum for PN symptoms, as well.
You may need to increase to 3200 or 3600 a day for symptomatic relief.
I think your meds need to be revised, and a different mix may help.