1999 Silverado, blinkers just quit working. Replaced the fuses and the blinker relay and they still won't work. Not sure what the next step is

 

Since you've already replaced the fuses and the blinker relay, the next things to check are the turn signal switch and the wiring. The turn signal switch could be faulty, or there might be a loose or damaged wire somewhere in the system. You can also check the bulbs to make sure none are burnt out, though that usually wouldn't stop both sides from working. If you're not sure about the wiring, you may want to get it tested to find any breaks or bad connections.