TJ, I had the same injury four years ago, except I got bolted off into the wall of an indoor instead of a fence. I was in a Sarmiento splint for a couple-three months till a decent callus formed on the humerus. Unfortunately, the incredibly incompetent local orthopedist I saw told me not to worry about the fact that I couldn’t move my arm at all. At the three-month mark he theorized that perhaps I’d damaged the brachial plexus. When I finally insisted on an MRI, it showed that I had actually severed two tendons in my rotator cuff, which were now retracted and possibly irreparable. Turns out that pseudoparalysis (a mechanical rather than neurological issue) is pretty definitively predictive of a massive rotator-cuff tear. Happily, I found a fantastic surgeon who did a very, very tricky repair (four hours plus in surgery) that eventually (within about a year) got me back around 60 percent of my normal range of motion, where I’ve held steady since. (I actually have to get the other shoulder done in two weeks, as all the compensatory overuse trashed it too, though much less severely.) The moral of the story is, be the squeaky wheel! If you sustained an impact great enough to break a long bone, you likely also shredded some soft tissue. INSIST on further diagnostics if you’re not improving!
Good luck! It’s a really miserable injury.