Switched to using mouse in left hand for work, right hand for gaming. Never looked back. Turns out mouse motorics are almost independent from human handedness.
To comment the article, depending on OS and mice, you will have trouble assigning different orientation to different mice. Usually if you want left hand mouse to have index finger "left" click, it will also switch your right mouse... and trackpad...
1. Don't power through it. You can easily cause permanent damage.
2. Trying different ergonomic changes can help. Two mice is a very interesting idea, and there's numerous other variables to try, and in different combinations, to see what works for you.
Get yourself 2 keyboards, each with trackpoint nubs, and a mouse and a touchpad! Probably the touchpad comes for free if your desktop is a laptop with a touchpad; mice are cheap -- there's a big tangled knot of them near where the desktop support people hang out where I work. The same goes for cheapo keyboards, though keyboards with touchpoint are a bit more thin on the ground.
For a very long time I used 2 keyboards and one monitor, just because everyone else used 2 monitors and one keyboard. I'd use one keyboard for my left hand and another for my right hand; I'd randomly nudge the keyboards around the desk until I was comfortable with the setup and then nudge them around a bit later, just because. Also I had 2 mice -- a big messy desk workspace.
Anyhow, it's not like we're stuck with PS/2 inputs -- USB lets you have as many input devices as you like.
Lastly -- there's a bug in MacOS that for some reason the meta keys of one keyboard don't apply to key strokes from another keyboard. So left keyboard / left shift key and right keyboard letter a would result in an a glyph; while with windows (and perhaps linux; haven't tested) you'd get the "correct" output of "A".
Right hand on odd numbered days, left hand on even numbered days.
Old Navy trick.