Of course, yes. High fever can lead to burning eyes. As we know that when you have a high fever, it can be the cold which cause that. And when you have high fever, your blood will become high too, at this moment, it will make your eye pressure high. Of course, it can lead to bloodshot eyes. But on the other hand, you also should know that it is possible to have burning eyes too, when you have high blood pressure and eye pressure. So if you have this kind of symptom, you should just be careful about it. Well, to make your eyes feel better, you can put some cool ice on your eyes, so that it can relieve your symptom. Also, you should eat a diet rich in fresh fruits and vegetables. You should know that these foods provide lots of antioxidants, which may help boost your immune system, especially vitamins A and C. by relieving your cold, your high fever will be relieved, in that way, your burning eyes will go away. Anyway, you can just take some measures to treat it.