Should I be worried if only one eye has discharge?

Both eyes are exposed to roughly the same environment, dust, wind, allergens, so discharge appearing evenly on both sides often points to something general affecting your dog overall. One eye reacting noticeably differently from the other suggests something specific to that eye rather than an environmental cause.

A stray eyelash, a small scratch from a stick or blade of grass, or a foreign object that only entered one eye can all cause this kind of asymmetry, and it is worth checking that eye closely for anything visible before assuming a deeper cause.

If a close visual check finds nothing obvious and the one sided discharge continues for more than a day, or comes with redness, squinting, or your dog rubbing at that specific eye, a vet exam can identify what a home inspection cannot.

Taking a quick photo of both eyes side by side when you first notice the asymmetry, then another a day later, makes it much easier to judge objectively whether the difference is improving, staying the same, or worsening than relying on memory, which is useful information to share if you do end up calling a vet.

Gently checking whether your dog blinks at a similar rate in both eyes, rather than favoring the affected one by blinking less or keeping it more closed, adds another useful data point when deciding how urgently to seek veterinary attention.