Is there any way I can fix my Apple Watch band from sliding? One side doesn’t click. Do I need to buy a new band?

I suggest you start by comparing the locking components on the two parts of the band, and the channels on the watch body into which they slide. I think there are 3 more likely possibilities, (a) the locking tabs on one part of the band are stuck, (b) the lock release button on the watch body is stuck in the pushed position, (c) we know from experience that a band fitted upside down may not lock correctly.

Also take a look at Change your Apple Watch band - Apple Support for details of the correct orientation of the band.