Well, it seems that you are quite worried about your health. So, as a matter of fact, I should tell you that there is little relationship between a throat infection and eye infection. However, according to some cases, we infer that an infection could affect other parts of our body. When a throat infection goes serious , it is likely to cause eye infections, because some disease has a lot of symptoms at the same time.
Yes, it is possible for you to get eye infection because of the throat infection because the throat nerves and eye nerves are interlinked. Once you have the problem at the throat, your immune system will be weak which will let your eyes get the invisible bacterium easily. You'd better go to see the doctor and accept the treatment.
Of course it is possible to get eye infection because of throat infection. Throat could be called pharynx in medical terms. Throat infection is the so called pharyngitis, which is caused by bacteria or virus in most cases. And for pharyngitis caused by virus, most cases are contagious. Pharynx is one part of upper respiratory tract. Adnovirus is a wide spread DNA virus, which could cause condition of respiratory tract, gastrointestinal tract, urinary system and eyes. So we could see adnovirus can cause throat infection, which make our throat tight, pain and coughing. With coughing, sneezing or hand touching, it is possible for this virus to travel from our infected throat to our eyes. It could cause conjunctivitis.