According to what you said, I should remind you that if everybody tries to expose their eyes to the sun, burning feelings would be inevitable, unless he or she got a pair of nice sunglasses with perfect lenses and ability to tackle UV. For the sun is much too strong for a person. If would not be wise for anyone of us to stare at the sun, which would give rise to some great damage to your eye health and vision.
Well, generally speaking, there are many factors which can lead to burning eyes, such as eye infection and high eye pressure. But for your situation, I think it may be because of the eye infection. At this moment, you need to try some ways to treat your burning eyes. For example, you can have some cold compresses, and put some cool ice or cool cucumbers on your eyes. In that way, it can relieve your symptom and make you feel well. Also, for burning eyes, high eye pressure can be fatal, especially in summer. So I will suggest you have a good rest and that can be good for your eyes. of course, a pair of sunglasses can be perfect.