Generally speaking, for some people, this situation is kind of normal. Anyway, you may not need to worry about it too much. First, as we know that the light is so strong that when we open our eyes to see it, and the light gets into your eye ball, so it will just make the eyes hurt. And also our eyes are so very sensitive that they will react to the stimulation from sun light. So when the sunlight gets into our eyes, it will make our eyes to adjust to it. According to some researches, sometimes, it will also make your eyes not just hurt, but also become watery. So for your situation, you'd better wear sunglasses to protect your eyes from the strong light. And also, there are many irritants in the air outside, so when you go out, your eyes are easy to be infected by them. Just be careful about it. Anyway, you should not make your eyes to be exposed under the sunlight for a long time. Or it can lead to many eye diseases, such as the red eyes, and dry eyes.
Too much bright sun lights may hurt your eyes because of the uv and other bad light in it. You could wear the pair of sunglasses to prevent from the uv. Or else, your eyes may feel the spots in the vision. You'd better not stare at the strong lights directly. In a word, you should protect your eyes.
Bright lights stimulate some cells in your eyes. Despite being inside of your eyes, there are some cells never see light. When you move from a lower light area to a brighter area, your pupils are still dilated. Hence the entering light is not focused onto the cells, which are in the back of your eyes. The bright light falls on those sensitive cells would cause your eyes be painful.