Yes, the tooth infection may cause the red eyes. As we know, the nerves in the teeth, eye, nose and other parts are interlinked. When one of them gets the infection, the other parts may get hurt. And the eyes may feel dry when you get the teeth infection which will easily cause the redness in the eyes.
A tooth infection is a complication of tooth decay.Red eye could be due to an illness, injury, eye infections, or other condition such as allergies.As far as i can see.you may have had an eye infection which a pocket of infection in the eye socket. This is a known complication of an infected tooth. The eye socket is next to the mouth and separated only by a very short distance. Provided the amount of swelling and eye infection is a good possiblity.