My attacks of Trigeminal Neuralgia were unmistakable. I was in the fetal position on the floor in complete shock from the pain, like an ice pick repeatedly jabbing down the side of my face.
I experienced this extreme on the left side only, but I've experienced the 'atypical' type TN bilaterally. The atypical, while painful, isn't near as painful as the 'classic' TN.
I'd imagine that people experience the pain differently, just as much as we all experience symptoms differently.
Definitely ask your neuro about it, but don't rule out a dental pain specialist. Mine was diagnosed by a dentist who treats TMJ and various pain conditions in dentistry.
Hope you're feeling better soon!