Where is the fuse box on a 1998 Monte Carlo?

What you need to replace here is the flasher relay. This is typically located on or near the steering column. You may need to remove the knee bolster underneath the steering wheel to access this. It's a fairly cheap fix, a new one is available for around $5-10. Fuses are not going to be your issue here as this is a separate relay not located in the fuse box.