Yes, it may. The eyes get twitching because the eyes get infection from the bad environment of dust or sand or because the eye nerves go in disorder. And the throat, nose and eye nerves are interlinked which the sinus infection may cause the twitching eyes.You'd better go to cure the sinus first.
As we know, sinus infection will cause enormous influence on people's daily life. Sinus as guards in the respiratory tract, as soon as it has problems, these organs, tissues, such as lungs, trachea and so on, will suffer a lot. And also it can affect the surrounding tissue, like the brain, eyes, etc. If the disease is severe, it can also cause a harm to people's life. In a word, sinus infection can affect learning and work, so you should receive the treatment early.
My mom has the same situation with you,she got sinus infection since several years ago,and every time the infection came back again,something would go wrong on her eyes and ear.Her eyes twitched too,so the doctor said it's a normal phenomenon.In a word, you needn't worry about your eyes,but you have to make yourself recover from sinus infection as soon as possible,just in case it will harm your whole immune system.