Yes, it can cause your eyes to swell. Generally speaking, when you have a sinus infection, there always is a small chance of an allergic reaction. And any symptoms that are new and potentially consistent with an allergic reaction need to be evaluated right away. A more serious allergic reaction might include swelling around they eyes or mouth, or trouble breathing. If you have the swelling around your eyes and have no other serious symptoms, I suggest you should go and see a doctor. On the other hand, if you have any of the other serious symptoms, or severe eyelid swelling, then you should go directly to the emergency room and not wait for an office appointment with your doctor.