It can as inflammation in the nose and sinuses can cause inflammation around the Eustachian tube, which is the tube that runs from the back of the nose to the middle ear and is responsible for draining the middle ear of fluid. If there is Eustachian tube dysfunction from nose or sinus inflammation, fluid can remain in the middle ear which can lead to dizziness.
Hello and hope you are doing well.
It's unlikely that sinusitis can cause dizziness. Your symptom of dizziness if its relieved by eating something, may indicate that you might be having episodes of hypoglycemia. Inadequate sleep can also cause tiredness, fatigue and dizziness. Other causes for these symptoms are inner ear infections; brain disorders heart problems, fever, stress, low blood pressure and anxiety. Please consult your GP who will examine you and may ask for blood tests for evaluating blood sugar and CBC.
Hope this helped and do keep us posted.