Is there anyway to repair holes in bricks without replacing the whole brick?
What do you mean by "holes". You mean someone drilled thru them or the surface has eroded to make the hole? One idea that comes to mind is to use a mortar mix that is colored close to your brick color. You can find colors at the big box stores or a brick supplier. The brick supplier may have more color choices. Before you fix them, wet them down until no more water soaks in. This way, the brick won't suck all the moisture from the patch which prevents failure.
They are single holes drilled in bricks. Someone attached shutters and drilled into the brick instead of the mortar.
I'd probably look for a caulk that was close to the same color as the brick, and fill it with that. Trying to make it as if the holes were never there would be a losing game.