Kboo, a lot will come down to the question how comfortable you'll be to ask help. I'm assuming you've been operated on one arm only and the other still needs an op? In that case I'ld strongly advice you to take a rollabout that moves VERY easily. Each correction you'ld have to do, even 'just rolling it', can cause you pain, damage or even a dislocation again. So also, don't try to help a person that's helping you store it. I know, easy said, but believe me you don't want to run the risks.
Hmm, should probably start explaining myself by now. I've got a hereditary condition that causes me to dislocate allover the place uncountable times a day. I know the op you've had, I've had them all.

I know the risks of the not operated arm yet, it's my daily life.
OK, let's return to flying. While official rules state 'they are not supposed to', I've never run into any FA not willing to stow my carryons. (allways have multiple, need 2 bags with medical stuff. I'm a real pain in the rear for those FA's, lol) I'm in a wheelchair so some FA's assume I can't stand (I've got the 'can't walk' status in my papers) and do it without me asking. Others will see me stand to transfer from the wheelchair to the seat. Non of them ever refused me help when I asked. I hardly ever need to explain, more than "I can't" isn't needed.
Now, you look a lot less 'not able to'. Is that a problem? Doesn't have to be. The sling will hint about one arm. Just ask for help and a quick chat about the other arm not in a sling being worse off. None of the people I know with my condition that walk on board have had help refused when asking help, sometimes briefly explaining they'll otherwise dislocate the shoulder. I had the same experience when I still walked on board, didn't look injured, bright young girl, but allways would ask for help with the carryon.
When flying; wear the sling. It'll prevent you from those little changes in posture that can hurt the shoulder after some hours. Also, during take off there is more pressure on your body. The sling might be comfortable at that point and landing, not just one the one arm but also on the other.
Really, don't worry or be afraid. I've never run into a flight with not even one FA on board that wouldn't help , let alone other passengers. Especially the american and asian based FA's were very helpfull.
A last resort? Take a bag small enough it'll fit underneath the chair in front of you and stow it there instead of in the overhead compartment. But don't feel the need to do so in fear of not getting help.