First question — is your car a 1992 or 1993 model, or a facelift 1994. Reason for asking is that they use different bulbs for the headlamps.
The first thing to do is ALWAYS to check the fuse of the headlamp circuit. Simplest things first.
If the fuse is removed and visually checked as being OK, then I would check power at the disconnected headlight plugs (rear of headlamps) with a multimeter, to see if power is flowing to the lamps.
If not, then you have a power interruption upstream. If you have power at the lamps, then you have either an internal lamp, or a bulb issue. I believe it to be the former, as it would be impeobable to have two main headlight bulb filaments go out at the same time.
Let us know what you find with the fuse situation (REMOVE it, don’t just look at it or rotate it in place) and with the power situation at the headlight plugs (both sides).
All power to the lights does go through the switch, and the turn signal stalk is also associated with the system. But let's get the basics first.
As far as I know, the bulb-out monitor relay in the rear relay portion of the fuse box is not a gating factor in the headlamp power circuit, and should not affect anything with regard to power going to the main headlight bulbs.
I will have to confirm the electrical pathway of the headlights via the electrical diagrams, but I do not believe that full headlight power flows through this relay, it only monitors system load to determine if a bulb is out.