I hurt my shoulder, and I'm looking at ways on how to prevent this in the future

Last week I developed a slight swelling in the neck and my right shoulder, which was followed by a stinging pain in my shoulder (so bad that I couldn't even sleep). It turns out that I developed tendinitis (inflammation of a tendon in the shoulder), according to the doctor.

I am on pain killers and an anti-inflammatory drug, and have to see the doctor again next Tuesday. Earlier this week everything was so sore that he could only do a crude diagnosis. He is probably going to suggest another round of Diclofenac and Paracetamol and/or physical therapy.

So far, so good, but I suspect that it was partly caused by my sax playing. I have been playing baritone sax with a sling for years, but I recently got a new one (to low A). With this sax, and the sling, I guess that I have to rotate my right shoulder slightly more backwards to reach the keys. That's probably not the only cause (dressing too cold while riding my motorbike to work might be a culprit too), but I want to prevent this from happening again.

How are your experiences with using a harness for baritone sax, instead of a sling? Is this putting more stress on the shoulders, or does it distribute the weight better? I already found out that a harness makes my sax hang more in front of me than to the side, which probably is better for the position of my shoulder. However, with the sling, all of the weight is on my left shoulder, while a harness will put stress on the right shoulder as well.

Any advice, apart from taking enough rest?

Thanks!