Well, I hurt my shoulder slinging last year and learned a lot since then... If I were you I would get a doctor to look at your shoulder and identify what you have going on. Once you know what's wrong it's easier to deal with it. You could also learn some rehab excercises and such. The targeted excercises are what helped my healing the most - put the work into it and don't be surprised if you can barely so the stretches at first. If you tore anything you prolly will never heal naturally but if you didn't hurt yourself too bad and just stressed your rotator cuff or gave yourself an impingement it's hopeful
My shoulder is still healing and I skipped this season of slinging with it.... Hoping for next year. In the meantime, I have become somewhat proficient at slinging lefty! I don't have the same power, speed or coordination yet but I am capabable of accuracy and moderate power left handed.
And ya like the others said keep to sidearm or underarm. Your shoulder throws best and most naturally with your elbow level with your shoulder. Too high you risk impingement, too low you stress the muscles around your armpit/pectoral area. Keep it level!!! I find the style the forum has named "afghan sidearm" quite a bit especially since it's not overly complicated.
Hope I didn't run on too much just trying to help!