Carbs can also contribute to sinus problems. I had terrible sinus congestion from inflamed turbinates, resulting in repeated sinus infections, sleep apnea, and general misery. I had to cut the carbs due to diabetes and got relief in less than a week. I can breathe better, sleep better, think more clearly, allergy season is less awful...but the docs still think it's all unrelated.
There's a lot of evidence that blood sugar control will also help cut down on seizures (see, e.g., the ketogenic diet, modified atkins diet, and fasting), but that is, so far as I know, medically unproven.
My allergies & sinus problems got significantly worse in the early 90s when I moved to a new city & state to start my working life after college. At the time I thought it was just exposure to new allergens, but in retrospect it's clear that that was also the moment that I became much more sedentary (working a desk job) and all the other symptoms that cleared up when blood sugar was controlled, also worsened at the same time: anxiety, depression, moodiness, poor sleep, short-term memory problems...
No matter what the docs say, it's all interrelated, they just don't understand it yet.