Is this the old body style Silverado or the the new GMT900 body style Silverado?
If it blows from the alarm or the panic alarm then the horns and the relay and the bcm are ok. That pretty much leaves the wiring in the collumn and the contact buttons in the steering wheel or airbag.
You'll need to remove the Air bag and try to ground the horn circuit to see if it blows the horn. The horn circuit runs through the SIR Coil Assy and if you ground the horn circuit at the coil and the horns don't blow, then the SIR Coil may be open and will be replaced. If the horns DO sound when you ground the circuit, then the wiring or the switches are defective.
To remove the Air Bag on the steering wheel, remove the SIR or Air Bag fuses Before you begin working on the system.
On the back side of the steering wheel, there are 2 access holes. Using a 3-4 mm T handle allen wrench , insert in a cross car (Horizontally) direction and slightly outboard (handle towards I/P) push in 40mm (1 1/2in) to engage release spring.
Remove the wiring and set the air bag on a workbench facing up.
Inspect the horn contact switches.
Hope this helps.