Can sinusitis cause brain swelling or a serous dealth problem I've been having a runny nose & watery eyes & lightheaded I'm worried?

Sinus complications. All paranasal sinuses except maxillary have surfaces that directly abut the layers of bone separating them from the brain and its linings. Brain, epidural, & subdural abscesses & meningitis can all result from sinus infection, as well as thromboses of venous sinuses of the brain. Have seen all of these. Although infrequent they do occur. Roof of maxillary sinus is floor of the orbit of eye.
Uncommonly. Most cases of sinusitis will respond well to treatment and sometimes even resolve on their own. A uncommon complication of untreated sinus infections is bone infection (osteomyelitis) of the forehead, extension of infection into the brain leading to meningitis (infection in spinal fluid) or blood clots in the brain. Also uncommon is extension of the infection into the orbit (around the eyes).
Not directly. The sinus cavities of the head/face are located in the facial bones & has bone separating them physically from the brain. In rare cases a sinus infection can extend backward through the bones & enter the space surrounding the brain. Fever, headache & stiff neck would be early & obvious with progression to death if untreated. I've read about it but never seen it in 3 decades.