Whenever I try to soft reset holding R + L and pressing Select or Start nothing happens. Do I have to do something to my DS or something?
I have the most recent update for Omega Ruby and Alpha Sapphire.
Make sure you are holding L and R when you push Select or Start.
It's more than likely that one of your bumper buttons are broken. A hard knock such as dropping your 3DS would be enough to break the buttons.
You can test if it's the buttons by running a simple test:
Exit the Pokemon Game, and whilst on the Home menu, alternate between pressing L and R - you should see each button light up the outlines in the bottom right of the top screen (The place where it says holding both should launch the camera). If one doesn't light up, you know it's that button which is broken.