It is definitely not a bad thing. I think it is rare to get so much feeling from music. I sometimes cry when I hear my favorite parts of certain music I love. You have a gift. You said you are not good at music, but even the greatest performers were "bad" when they started. However, they had the ability and special talent to feel music in ways that can usually never be developed unless you are born with it.
You should keep working on your singing or perhaps taking up an instrument. Once you master the technical part with lots of practice, you will shine bright because you have so much feeling when it comes to music. You might also be wonderful music composer some day.