I know a couple of guys that can play with both hands pretty well. One of them also did the switch due to a temporary injury. Now he throws with whatever hand neccessary on a hole. So it is definately makeable. I have tried a couple of throws with my left hand and i felt like a three-year old. It depends on your coordinational skills I would guess.
If I were you I would definately give it a try, maybe you will not quite reach the level of play you had with your strong hand, but it might still be a lot of fun if you start right now with your friends, so you can get better together with them as they also develop a better game.
I honestly have no clue about any medical stuff, but I have had a very positive experience with doing stretching. I was playing this winter (there is also a short threa din the injury section) and I had a tournament weekend where I played 40+ holes three days in a row in pretty cold condition. Apparently I wasn't warming up correctly so that increased the effect of strain on my muscles. Anyway, when I got home I had a really really sore elbow and went to the doctor right away, so it wouldn't get worse. He showed me some stretching exercises that I should do regularly and since then I haven't had any problems with my shoulder. However a couple weeks later I had a sore wrist and shoulder due to playing too much (or with a wrong form) disc & ball golf.Went to the doctor again and he showed me some excercises for my shoulder and gave me a bandage for my wrist. Again since then, no problems.
I would think you have already tried that, but I just wanted to share it in case it might help
In every case I hope you get on well with playing and hopefully someday your right shoulder will do what it's supposed to again.