Well, yes, it is possible to have dry eyes because of hay fever. According to some researches, when you have hay fever, it will lead to disorder in your body. And in that way, it will just affect your eyes, leading to some eye problems. For example, it will just cause dry eyes. And your will feel dry, or itchy. In some cases, you will get red, bloodshot eyes too. For your situation,you can choose cold compresses, and repeat it several time. Besides, you can just apply cool teabags under your eyes, which can be beneficial for your eyes. Of course, seeing the eye doctor is also essential.