I know that the Nintendo 3DS is region-locked. It will not let me play out of my region games. But there is an option of changing the region in the Nintendo 3DS's setting. If I change the region there will it allow me to play the games of that region too?
That setting will only change eShop region.
This will let you access different software listings on the shop, but you won't be able to play physical copies from that specific region. You are tied with the one you have.