Have you consulted with your orthopedist yet? I'm right-handed and did a number on my left shoulder last April where I was sure before the visit I'd need surgery. Barely slept for days because of the pain and had numbness from my elbow to my hand. I finally capitulated and saw the doc when it went from bad to worse. No detached tendons thankfully, and while surgery was an option, he recommended a course of steroids followed by PT to see how I'd feel first. Stuck with it and I feel much better. I have full strength again in most areas, but I'm aware of which angle I did the damage in the first place, so I'm mindful to adjust around this still somewhat vulnerable area. I've tweaked it a few times, but have been able to just shake it out like any other minor tweak to a muscle group.
What allowed me to fish consistently again after a few months was modifying my casting stroke and using rods with shorter handles. Basically, with short handles I can isolate my upper left arm by keeping it tight to my side and pull the butt-end of the rod using only my elbow-to-wrist. The shorter distance between my hands during the cast facilitated by the shorter handles greatly alleviated stress on the injury. I can still generate good casting distance this way, and I feel no discomfort at all as long as I remember myself. Even when I forget occasionally, I'm pretty much OK now, so it's not a problem. However, as with any other old injury I've had, I must be mindful to work around this one in order to avoid inflaming it. I can still move like a chimp when I want to or need to, as long as I mind the stress angles which caused my problem in the first place.
After this experience I came to learn that several people in my orbit with far worse situations than mine chose the given option of PT instead of surgery and are fine with their choice. You may need surgery no matter what, but if the option for PT is offered as a viable alternative, you need not be as skeptical as I was beforehand. I really thought my goose was cooked, and that there was no way I wasn't getting cut, but I was wrong.