Ache (burning) in back right side of head for 3 weeks when I inhale through nose, no pain when I breath through mouth. Occipital neuralgia?

Unlikely. Although pain in the back of your head sounds like occipital neuralgia the fact that it only occurs when you breath in through your nose does not fit. Breathing should have nothing to do with it. I would see a pain specialist.
Probably not. That doesn't sound like occipital neuralgia to me. I would go see a regular doctor for evaluation. He might want to refer you to an ENT specialist.