They don’t want you to work in part, because muddling through and doing what you can will undoubtedly irritate your arm and extend the length of your injury.
They have complete faith in you, take that to heart, and enjoy your time off however you can!
Just don’t irritate your arm
Have fun, and stop worrying already!
Go on a mini trip! Enjoy your time off instead of concerning yourself of how well you feel despite your obvious handicap.
My wife injured her shoulder in September, spend three weeks in a sling, and has been working with physical therapists twice-weekly ever since to recover from “frozen shoulder.”
So, OP should probably at least ask the doctor about the advisability of taking steps to prevent that, lest it become necessary to treat it.
Go, have fun! Take pictures. (if you can do that with one arm in a sling)
Just to elaborate on Kopek’s point, just because you feel fine doesn’t mean that you are fine.
You have earned the sick leave & you cannot give 100% at the office.
Don’t feel guilty. Do keep any activities low key & get plenty of rest. (Somebody upthread suggested "ride your motorcycle. Nope.)
I’d be tempted to veg out & use that Netflix account (which* I *already have). But you sound like the sort who might get busy “fixing” stuff around the house. Involving tools & ladders. You’d be safer in a nice, quiet museum.
Yes, take a trip, but don’t post on Facebook! 