Well, I used to have the same feeling with you, and my situation is resulted from playing too much video games without any breaks. So, what I recommend is that you should take some breaks at intervals, and try to get some eye drops. If the situation continues , you need to see a doctor , for there might be some serious problems then.
When you blink and your eyes feel burning, you need to pay attention to. Your eyes may have the coming invisible bacterium which causes the burning symptom. You should use the eyes drops with anti-inflammation to treat your eyes and make your eyes feel comfortable. You could also use the warm compress to make your eyes feel comfortable.
Eye irritation can always cause such condition. Burning, itchy, pain and redness are usual symptoms of it. And when you blink, the focus will not on minors and sore come into being. Bacteria also catches such chance to damage your eyes. Home remedies to control your burning is drop the counter eye drops and wash eyes with warm water. Put poor cosmetis far away from you.