Many women feel moody and can't hold back their tears in the days after giving birth. You've got a newborn you are "in love" with your baby and so happy to be a mother but you are also exhausted and the changing hormone cocktail in your body is playing games with your mind. The baby blues is a well-known phenomenon. And yes, it is completely normal.
The baby blues amounts on a combination of physical and emotional factors. The hormones we already mentioned are most probably the biggest contributor to that feeling of being blue. There's also feeling physically rough after childbirth (including vaginal tears, perhaps) and having experienced some sleepless nights with your newborn. And then, there is the fact that parenting is no longer theory for you.
Now that you are a mother, you may be full of worries for your baby's future and concerns about what kind of parent you will be. The baby blues is a short-lived obstacle. By the time your baby reaches two weeks, you should be over those mood swings and the urge to cry at the sight of a "touching" TV commercial. Unless, of course, you are normally prone to crying at those kinds of things.
If you are feeling much more than the urge to cry for short times a day, and have persistent feelings of depression, doom, general pessimism and a lack of enjoyment in life and your baby, you may have more than the baby blues. And if your baby blues goes on for a long time (like, more than two months) you should definitely see your doctor as well. Postpartum depression is a much more serious beast than the baby blues. There is no shame in getting it though, and thankfully help is available.