All of his symptoms are probably related to the same infection. It sounds that he probably does have pink eye (conjunctivitis). This and his other symptoms could be due to either a viral or a bacterial infection. With him having this combination of symptoms and the fever I would recommend that you take him to his pediatrician tomorrow.If this is bacterial then he would benefit from antibiotic therapy. If viral then at least the doctor would have a baseline for possible future comparison should his recovery not follow the expected rate of improvement. Also with cough plus fever it is important to listen to the lungs to ensure that there are not clinical signs of pneumonia.
I hope this information helps. Further questions are welcome if you have others. If my answer has been helpful and to your satisfaction then please remember to press the "ACCEPT" button. Thank you and Best Regards,
Anthony Bray MD