The signal going from the mp3 player to the earphones is entirely made up of electrical impulses, which are converted to audio signals (by vibrating air). At no point is any electromagnetic radiation involved.
(For the pedants: OK, there's actually an almost infinitesimal amount of electromagnetic radiation because all electrical currents produce such radiation but it's much, much, much less than you'll be getting from your TV, your computer monitor or even your desk lamp).
If your mp3 player uses the earphones as an aerial for its radio then there's a tiny amount of electromagnetic radiation being absorbed into it but your body is already receiving tiny amounts of electromagnetic radiation from every BBC and commercial TV and radio station in your area anyway (and VASTLY more electromagnetic radiation from your mobile phone).
Stop worrying. The only risk you face is that of potential damage to your hearing if you set the volume too high!
Chris