The noise you here is the electric fan. Most cars secondary fan will kick in as soon as the air conditioning is turned on. Yours has probably always made this noise, but since the check engine light came on, you are now being sensitive to noises.

BTW, the check engine light is a result of emissions codes. Most likely an O2 sensor but could be as simple as a loose gas cap. Either way, it is safe to drive the car until you get it back to your service department.