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I tore my rotator cuff while boxing in 2005. I was throwing a clumsy right hook and overextended my shoulder. It was a partial tear, not all the way through. Because it was only a partial tear, I did not need surgery, and it has healed successfully. For several months after the tear, however, it was painful, and I couldn't really do much with my right arm. I had to build it up back slowly and had physical therapy. I didn't box at all that first year of recovery, but worked out with weights and machines and was careful to start with light exercises and build back up slowly and carefully.
However, now, 3 years later, it is well healed and I am able to box or do other forms of exercise.
Each case is individual. First of all, make sure you need the surgery. In many cases, this is an injury that heals, but you will need to build your shoulder back up slowly and gradually--no boxing at first! Only after you have built your strength and flexibility back up slowly and cautiously through physical therapy and a gradual exercise program, then you may very well be able to box again!