My headlights on my 1999 Buick Century don't work but my blinkers, parking lights, and high beams all do. Any idea what it could be?

You answered your own question-- possibly

A failed high beam switch !

check low beam fuse when switched on if it has voltage registering across the fuse ,if there is voltage across the low beam RHS fuse then it is possibly a pinched wire from the headlight running back towards inside of the car

I know of no module called the headlight module. Do the basic tests of the main head light switch for proper power and grounds at the connector.

Did you check the headlight switch ?
The high beams working bypass the headlight switch so you can flash to pass another car.

replace the light switch

you have a ground wire loose or need new bulbs bc they r fixing to go out or the autonator isnt chargeing like it suppose to be

Your high beam switch is bad most likely.

no low beams on my 1999 buick century change headlight bulbs and still no low beams

Go through all your fuses, Dim lights run on a separate fuse.

where is the relay headlight switch located on a 1998 buick century