Alli, this happens because the software you are using on your computer doesn't really rotate the image. Instead it only "shows you" a rotated image. My first guess is that you are using a Mac, but it is possible that some Windows programs could be doing this too.
This auto-rotate feature is a pet-peeve of mine, because it misleads the person into believing that the picture will be oriented properly when they share a photo with another person using a different computer (or posting to a website). The software thinks it is helping you by auto-rotating the image you see on the screen, but unfortunately it leads many users into believing that it was actually rotating the source image.
I don't know if you can override this feature or not, but if not, then you will have to use a photo editing program that actually performs a true image rotation.