When I broke my wrist (many years ago), the hospital didn't initially see the break on the X-ray (although they did a fortnight later) and only strapped my wrist very tightly on the assumption that it was a strain. The following day I asked my GP whether my fingers should be swelling, as they most definitely were. He made some very disparaging remarks about the A&E staff, asking "Didn't they think to give you a sling? Your wrist needs to be kept elevated!"
So I'm wondering if you're in a similar position, where the hospital has failed to provide you with the sling that you need? (NB: If so, note that it needs to be an elevation sling, not an arm sling. i.e. the one on the left of the picture here:
https://pbs.twimg.com/media/C9h9RfkXUAArUHC.jpg )
Whether I'm right or not though, I hope that you're fully fit soon!