I bought some touch up paint that is the exact same as what was originally used, but it looks different?

Megan is correct but also the sheen changes as well, if you used a sheen. You will probably never get the two to match I'm afraid. But try what she said and use tsp, non-rinsable, to clean and not a multipurpose, or you might present yourself with new problems! If that does not work, just start over and repaint the wall.