I don't know why the garter stitch edge at the bottom is causing the afghan to curl.
Maybe it needed more rows of it to tame the tendency to curl. I don't know what you can do about it after the fact but you can use a short row every once in a while along the sides on the garter border to prevent the thing from pulling up. How often you would need a short row I have no idea, you'd just have to experiment a little and put one as needed.
What fiber are you working with? It seems like a bramble stitch afghan should be doable, but I have not done one.