I was told that it's my brake light switch that needs to be replaced

If all of the lights are out in the back I would venture to say that the brake switch is not the problem. It will only affect the brake lights and not signals and taillights.

If the taillights and turn signals still work you might look at the switch for the brake lights after you check the fuses. The switch is located on the brake pedal and is up under the dash. Pretty straight forward on removal. I would test it first with an ohm meter after removing the wiring connection.