No, this is not a sign of eye disease. It is normal for your eyes water when you watch ghost stories. Your eyes well up, because you are in a state of icy disbelief. There are so many things which are beyond your brain and comprehension that you brain is irritated to water.
Well, in my opinion, it can be because you are scared by the ghost stories. Generally speaking, watery eyes can be caused by many reasons. For example, watery eyes can be a sign of dryness. As we know that tears are for lubrication and for keeping your eyes clean. So when your tear glands don't work in a wrong order, it may develop dry eye syndrome. In other words, if your eyes become dry and uncomfortable, the tear glands react by producing large amounts of tears. And it can be the most common reasons. But on the other hand, eye infection, allergies can also cause watery eyes. And for your situation, scary emotion which can just irritate your tear system can be another reason. And in my opinion, your eyes will be fine, after you have watched movie. So you do not need to worry about it.
It is not a sign of eye disease, and you need not worry about it. When you are absorbed in reading ghost stories, the horrible things activate your autonomic nervous system that can make your eyes watery. Besides, when you are reading the ghost stories, you must be thinking about it and subconsciously put yourself in the scenes of the stories. At this time, your eyes become watery and your hands may also shake. There is one more reason for this condition. You are so scared by the ghost stories that your eyes start to tear up. It is also unnecessary for you to feel embarrassed, for a great many people share this problem with you