Many people who have eye allergies may suffer from headaches at the same time. So they often think that eye allergies will lead to headaches. But they may be caused by the same reason. When spring comes, many people will get eye allergies. They are caused by an abnormal immune response to the pollen grains. The immune response may results in inflammation in the eyes, nasal cavity, and sinuses. We will suffer from headaches at the same time.
I think eye allergies will not cause headaches. But if your eye infection spread to other parts of the body, the inflammation will bring some migraines. I can give you some suggestions to deal with your eye allergies. You can avoid the pollen grains. How about wear a pair of sunglasses when you are in the outside? If the sunglasses cannot prevent from allergies, it can also prevent the harsh light and UV of the sun.