Well, generally speaking, it can be normal to have itchy eyes after you have taken the eye exam. In my opinion, when you have an eye exam, it will make your eyes focus on the points for a long time. And then the light can go through your eyes to check it. In this way, it can lead eye strain. And then lead to eye pressure. As we know that eye pressure can lead to some eye problems, such as itchy eyes. Also, you should know that if your eyes are not accustomed to the new situation, it can react as the itchy eyes too. So just console with your eye doctor, and he can just give you some advisable suggestion. So you should not worry about it.