Fighting an infection takes a lot of energy. If you have a fever, are not drinking enough water, or are taking decongestants that dry you out, you may become dehydrated. This is a common secondary cause of dizziness during illness.
Most cases of sinus-related dizziness will resolve as the infection clears (usually within 7 to 10 days). If the dizziness persists after your other sinus symptoms have gone away, or if it is severe enough to prevent you from standing or walking, consult an otolaryngologist (ENT). You may be dealing with a primary inner ear issue rather than a sinus issue.
If you are experiencing true, violent spinning, it is less likely to be a direct symptom of a simple sinus infection and more likely to be a secondary complication (like labyrinthitis) or a separate inner ear disorder.