Is it true that a white blood cell count can show you have brain swelling?

Maybe: Patients with a concussion or cerebral edema can often have an elevated white count but an elevated white count alone is not specific evidence of brain edema.

Not specific: White blood cell counts are an indication of infection. Brain infection can cause this, but i would assume a cluster of other symptoms that are significant would make one look to the central nervous system, rather than a WBC count. Medical attention is required for a proper differential diagnosis. Good luck!