Not really, I can not make sure that sinus infection will cause bloodshot eyes, but I know that sinus infection are always happened together with puffy eyes. Puffy eyes are a common symptom of sinusitis often blamed on lack of sleep or general illness. In addition to puffy eyes, sinusitis problems may cause a dull ache or feeling of pressure in the eyes or across the middle of the face, nasal congestion, postnasal drip, raspy voice, loss of sense of smell, fever, nasal discharge, bad breath, coughing, sore throat, snoring and fatigue. Most cases of sinusitis are caused by infections, but allergies, exposure to indoor or outdoor air pollutants, excessive indoor dryness from heating and air-conditioning, and structural abnormalities are other possible causes. You can reduce or eliminate most cases of sinus-related puffy eyes at home or with over-the-counter medications, but some cases may require professional care