What will it cost in parts to get my 1990 jeep cherokee back on the road?

Hello, With any wiring issue of the caliber, there is always a chance of extended damage beyond what is noticed. I doubt the relay or switch was the issue because there should be no way a relay would get hot enough to flash into a fire. Replacing burned sections of wires, especially on an analog system like headlights, is cheap and easy, but you may still have a problem existing. Start by repairing the wires with new sections, crimp fittings, and heatshrink tubing. Afterwards, replace bad fuses and relays, and diagnose the problem. That is the only way you'll know how to quote the job.