If the shinx is actually living with you at this point, it’s not only unlikely that you’d have to worry about its mother, but it’s also very likely that the shinx isn’t as young as you think. Because of how intense battles between wild pokémon can be, mothers rarely let their young stray far from their nests or dens. Likewise, shinx especially need to nurse until they’re independent enough to hunt and survive on their own, so if this shinx weren’t ready to explore the world or perhaps find a trainer, you would have encountered the mother by now (or the shinx would be dead).
In short, it wouldn’t hurt to help your brother catch this shinx if it wants to be caught. I would advise taking it to a center afterwards to have it looked over and to perhaps, if you’re curious, find out roughly how old it actually is.
Best of luck!