I have a 1998 Buick Century Limited and my driver's side headlight won't work. I replaced the bulb and checked the fuses under the hood and everything is checking out. My blinker still works.

Not a fuse if right side headlight comes on, it is probably a bad connection or broken wire, with the bulb plugged in the socket, move it around with the lights on, still don't work continue up the wire to the next connection and check it out. It is nice to have a test light for this kind of thing, then you can figure out where the power stops.

Could it be the headlight switch that has gone bad?

Not sure, maybe, did you see if there is power in the line into the socket? A test light is cheep, alligator clip one end, sharp steel probe on the other, with a light in before the probe, just connect alligator clip to ground, test (probe) to a known power source to make sure there is a good ground connection, check power line to the bulb, follow it up until you find power.

Neither one of my lights work, got new headlights, checked fuses, nothing works.