Its your car. Its up to you to know what service is due when. A timing belt is not a lifetime component, its a service item. If you didn't get proof when it was last changed, you really should have looked into having it done sometime in the last year and a half since you bought it. The Fiat Bravo/a 1.6 has a relatively cheap timing belt to change, but is also a very unforgiving engine with the intervals. It needs doing regularly and with Fiat, it should be done before the interval is up, not after.
You could have a trusted mechanic pull the head off and see what damage you've done. You might get away with a new head and timing belt/tensioner. If it's damaged the pistons you're looking at a whole engine. Depends how much you like the car really. But the parts are not hard to come by for Bravo/a.
With a second hand car that's a 1998 to boot, you can't expect the garage to have a crystal ball and know if your timing belt might fail. You need to know when it's due to be changed and take care of it yourself...