I disagree with the hammer swing comment, but agree with everything else. There is a reason that casting instructors forever have had people hold something to their body with their elbow, it works.
However I'm not a proponent of that and self taught, my elbow was dancing all over the place when I learned to cast. The single thing that helped me the most was that I could let my elbow travel forward and backward, but never change elevation. Think of your elbow as if it was on a shelf. It can move forward and backward but can't drop below the shelf. Anytime you drop your elbow you slow down your fly line which is pretty much the opposite of what you want to do.