Yes, of cause, it is quite possible. Sinus infection or sinusitis refers to the inflammation of the nasal passage and sinuses. Patients with sinus infection might have a headache and pressure in eyes, probably with a coughing, sore throat, fever, bad breathe and thick secretion in nasal cavity. It would lead to eye problems easily, puffiness or eye infections. Eyes are very near to nasal cavity and they are connected together with internal passages. It is easy to spread the virus or bacteria to eyes. It can also cause a dull ache or pressure in the eyes. The thick secretion might gradually lead to tear duct blocked too. During your sinus infection period, don't rub your eyes with hands or dirty handkerchief. You can get a nasal washer to keep your nasal passage clean and free-flowing. Take medications as needed.