I didn't even Google this. I don't know if there's some study or any scientific evidence for this and I don't care. While I'm no rocket scientist, I have been able to bench 600 raw in three weight classes, 900 equipped, total pro raw in a full meet, and lose and keep off over 100 lbs. My advice is mostly anecdotal, but I get the job done.
Now that I have finished tooting my own horn I'll get to the actual advice. I have lots of issues with my shoulders, but one of the most nagging is arthritis on my dominant side. While making popcorn I reached up into the microwave with my right arm and as usual, it aggravated my shoulder.
It was then I realized that perhaps using my left hand might help my right shoulder feel better. Granted, constantly remembering to do this is easier said than done. However, without dragging this out too long it has made a difference. Just making a conscious effort to use my left hand while carrying items and especially when reaching up to grab things has helped. Who knows how creative you can get with using your non-dominant hand...