Yes, it normal. One study estimated that 6% of those between 6 and 18have this problem. This condition is called anisometropia, means two eyes have an unequal refractive power. Someone is in different states of myopia, hyperopia, even antimetropia. And the usual correction is to wear contact lenses.
Ok, looks like there is something wrong with your vision. From what I know, it is possible that one of your eyes is different from the other one, because some bad use of our eyes, and some infections may deteriorate your eye health. And normally, there would be some slight differences all the time. Just try to take some medical checkup and protect your eyes as much as possible!
It is very normal for eyes to have different descriptions. I have the same experiences. My left eye has -6.00 description while my right eye has only -4.00. It may feel uncomfortable to wear glasses with such different descriptions. However, as you have been used to it, it won't affect the daily life.