Well, generally speaking, of course it will make your eyes become red. As we know that red eyes are common and usually occur due to eye irritation. You should know that sinus infection can cause your eyes bloodshot, by increasing the pressure inside the blood vessels. In this way, your eyes will turn to red and make you feel bad. And also, you should know that there are many reasons which can cause red eyes, such as the eye irritation, eye energy and lack of sleep. But for your situation, we can say that there is something to do with the sinus infection which leads to red eyes. In my opinion, maybe you can have some eye drops or put some ices on your eyes. If the situation is still serious, I suggest you should go and ask the eye doctor for the details.