This is what helped me the most. In my case, having the elbow at the same level as the wrist and a mousepad with cushion makes it so that my arm from elbow to mouse is roughly a straight line... IOW, no bent wrist. That solved my sore wrist issues. That may require adjusting your chair/desk heights, if possible. Same thing for typing.
I tried for few minutes switching to left side. But that is not that comfortable. Particularly I want some speed in typing etc. at least some help if we can't use one hand.Have you just tried switching mouse hands? I did it for two years at work. It of course helps and it frustrating at first, but you never acquire the dexterity of your dominant hand.
Speaking of posture, I once dealt with tendinitis in my right hand from drawing too much on the computer at work: lots of tension buildup and bad chair-desk setup. Anyhow, I bought a special chair that helped a lot.as Ina mentioned please check your desk and chair first. Your arm should rest naturally on the desk starting from fingers to your elbow. Your posture should be straight with feets on the ground.
I use the same mouse, it's good -- also on my third one. They do last many years.
A mouse pad with a wrist cusion also helps a lot. I use one along with a keyboard wrist rest cusion, and a chair with an arm rest a desk level.