if its a 5600 series crank,10 spd, then yes one side could make noise and not the other. the BB spindle is one piece incorporated with the drive side crank the bearing cups mount outboard of the BB tube and the drive side may not have enough grease. Are the pedals new? and were the spindle threads greased? a pedal that has low grease will start to make clicking or creaking sounds under pressure. The third thing I would rule out is your saddle a click from a loose bolt or rail can project downward.