Where do you here the clicking sound ? in the door , behind instrument panel ? I don't think a blown fuse would do this , possibly a relay ! do you know what a relay is ? This is Chevy factory service information !
Door Lock Operation
When the body control module (BCM) detects a transition of either of the door lock switches to the lock position, it switches the door lock actuator lock control circuit to voltage. Since the lock actuator unlock control circuits are at ground potential within the BCM, the door lock actuator motors transition to the lock position.
There are three pcb relays integrated into the instrument panel fuse box ( non replaceable ) door unlock pcb relay drivers door -door unlock pcb relay an door lock pcb relay ! The BCM controls these relays ! Do you know what a BCM is ?
The DR/LCK fuse supplies battery positive voltage to the I/P fuse block for the door lock system. The body control module (BCM) supplies and monitors a reference voltage to the door lock switch through the door lock switch lock/unlock signal circuit. The door lock switch also receives a constant ground source. If a door lock switch is placed in the lock position or unlock position, the reference voltage is taken directly to ground and the BCM detects the voltage drop on the signal circuit.
The BCM, upon receipt of a door lock switch lock or unlock signal, will switch the appropriate door lock actuator control circuits to battery positive voltage. The opposing side of the door lock actuators are connected to ground internally within the BCM through the other door lock actuator control circuit and the doors will lock or unlock appropriately.
With out have a factory GM tech 2 scan tool ,It would be best if you took this to a Chevy dealer . The first part of diagnosing this problem is to hook up a scan tool !
How to test computer controlled door locks