Yes, it is normal. If you have the habit of leaning on the bed to read novel for a long time, your leaning side of the eyes may get higher prescription then the other ones when you get short sighted. It is normal. You need to adjust your habit of using your eyes, including the posture and so on. You could wear the eyeglasses to help you get the right vision.
Yes, it sometimes happens that the eyes of a person have different eyesight. There are several reasons for this phenomenon. First of all, you may usually lie on bed on one of your side when you are reading a book or watching TV. This kind of habit will make your eyes see objects in different distance. As time goes by, the crystalline lense of your eyes will get use to different distances, thus making your eyes have different visions. Besides, if the posture when you are writing is wrong or abnormal, for example, writing with head inclined, will also lead to different eye sight of your eyes. In total, you should pay attention to your habits of using eyes in case the condition gets worse. Eat more foods rich in vitamin E which is good for your eyes. Do some eye exercises regularly and allow your eyes to have adequate rest. If necessary, use some eye drops. The most importantly, do not lie on bed when you are reading or watching TV, and sit upright when you are writing.
Well, sorry to hear that news. But from what I know, currently, a lot of people would get that problem, too! Because nowadays, people from all walks of life do not care much about their eye health, thus, they would make bad use of eyes and even damage them without knowing that! Anyway, you have to pay attention to your diet and rest, also, try to visit a doctor and get some method of mydriasis to treat your eyes.