It's a bit tricky to know what the buzzing sound is without hearing it. When I've got a disc in all I hear is the disc spinning (although it sounds like mine has got louder over the past year). So it may not be anything to worry about. I've also personally found that some of my discs sound different to others when running.
However, if you're worried about it, I suppose there is no harm in calling Nintendo for advice. Just carry on playing it and enjoy yourself for now I would say. If it breaks...it breaks! If you got it in January it should still be under warranty for a few more weeks.
I've been worried about my DS and Xbox packing up recently as well. But I've just come to accept, it's not the end of the world if they do break.
Hope that helps (a bit)!