Am I left or right handed?

I think you are ambidextrous; you are neither right- nor left-handed. Most people define the dominant hand as the hand that one uses to write. Since you write with your left hand, that would make it seem that you are left-handed. However, the fact that you mostly seem to use your right hand for sports argues that you are right-handed. Don't let this trouble you; as an ambidextrous person you have many advantages like being able to switch hands.