Yes, it is possible for you to get the broken blood vessels eyes because of the sinus infection. Since you get the sinus infection, the eye and nose parts are interlinked. That is to say, the eye nerves will be affected to some degree. The eyes may easily feel dry. That is the main reason to cause the broken blood vessels for eyes.
Hello, sinus infections will not directly lead to broken blood vessels eyes and cause the surface bleeding on the eye. What you mean may be the symptoms of subconjunctival hemorrhage, which is the bleeding on the eye. The looking can be very scary, but it's not a serious problem. This kind of problem often tends to happen after frequent sneezing, coughing, and rubbing the eye. What' more, high blood pressure or blood thinning medicines can also be the reason.