Well, it would not make people feel tired when applying eye makeups. And from what I see, perhaps your problem is resulted from some psychological effects. Maybe you should just get rid of those makeups until you feel much better about your health. Try to get some good rest and vitamins, and make sure your makeups are of great quality and reliability.
Yes, it normal. I also have this experience and even serious. Every time, I wear eye makeup, my eyes feel tried and itchy. So I always want to rub. I asked salesgirl, she said my eyes are sensitive. Makeup contains many chemical substance, most of them is harmful to health. I suggest, if it's not necessary, you'd better not make up. If you have to, later you must use makeup remover.