Yes, Flaco, it is normal. You are feeling your emotions which is a very good thing to be in touch with. The feelings themselves are terrible when they occur but the process you are going through is part of the healing, the opening up and letting go of your emotions instead of stuffing them down inside. This in the long run is good.
As to music that stirs emotions: due to this very thing there is music that I cannot and will not listen to. At the time it is OK, but after awhile it is not healthy to re-live and give energy to these emotions unnecessarily. What I mean is, feel your feelings as they are but try to resist staying in them too long and purposely. I know of this because I have done this too often in my life.