Well, yes, it is possible to have burning eyes when you suffer diabetes. And according to some researches, there are some common symptoms which can occur, when you have diabetes. For example, eye floaters will be possible for diabetes sufferers. Also, burning eye is another one. By the way, in some cases, itchy eyes can be possible too. For burning eyes, you can just get a soft cloth with cool milk, and then put the cloth under your eyes. In that way, it will be effective. Also, you can have some cold compresses, and put some cool ice or cool cucumbers on your eyes. Of course, eating a diet rich in fresh fruits and vegetables which provide lots of antioxidants, especially vitamins A and C a will do a good job to your symptom. Anyway, just have a try.