What horn do you have? The trumpet ooga style or other?
Assuming you are running 12 volts. If you damaged the horn I seriously doubt it was from using 12v for so short a time. As you saw a 6v horn is very loud on 12v and with short periods of usage should last longer than you do.
I agree with Tiny. It has been proven here many times. Metal vibration plate, big internal contacts and electromagnet wires can take 12V. Short bursts.
As Tophat says, check output of relay, but quickest way is to check horn positive terminal to see if 12V is getting there.
If 12V at horn and horn has good ground connection:
Take horn to bench or fender. Take off all horn wires and install direct hot from 12V battery and direct neg from battery. (no relay) Tap the neg for a second to test. Feel horn while testing. Any noise of vibration is a good sign. There is usually a adjustment screw/bolt to change the pitch. Try turning it. Could be that horn is just rusted or corroded. Could be contacts inside are "frozen" open or "frozen" closed. Check continuity between pos terminal and horn case. (power off). If horn has only one terminal (pos), be sure the ground test clip is on a shinny clean metal spot of horn/bracket. Be sure positive terminal insulator is still insulating.
I assume if there is a fuse, you have checked it. Assume a 12V relay.
You can test on the bench with a 12V battery charger as your power supply. Short bursts.
If all else fails, if you can't take it apart, before discarding, hold in one hand and tap all around on it with a soft blow hammer in the other hand. Increase impact after testing. Then throw it across the yard, and test. Then throw it away and yell "honk" out the truck window.
