the sinuses go all through your face so it's possible that there could be a connection between them and the tear ducts. i'd have to look at a diagram of the sinus cavities to be sure. however since tears drain partially down into your nose mucus from the nose could possibly force it's way up through your tear ducts. this could happen if you have some kind of blockage in your sinuses from the infection.
why would mucous suddenly come through the tear duct when blowing my nose with a sinus infection?