Hard to say exactly since we don't know if these headlights are part of the daytime running lights circuit or the regular headlight circuit.
But you can check the headlamp relay, which is in the relay box under the left side of the instrument panel (along with the fuses). The headlamp relay is in position #1, upper left hand side of the relay assortment.
If its the Daytime Running Lights, there is a DRL module on the left fender, back against the firewall, in the engine bay, and maybe that's gone crazy. You'd need someone to point that out for you, though, since it is near other relays such as AC Clutch, and is also near the air bag wiring, so you don't want to go pulling out the wrong thing.
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