Yes, it is possible to get one red eyes. Usually, the red eye is caused by conjunctivitis. So, you shall be careful, or it may also affect to the other eye. You can treat your eyes with antibiotics. In fact, antibiotics are the most common using for infective conjunctivitis. As far as i know, chloramphenicol and fusidic acid eye drops are the most common antibiotics for conjunctivitis. Nevertheless, you'd better check your eyes first to find out if conjunctivitis caused the red eye. Hope this can help you.