Then at some point in childhood, I don't remember when, I switched to my left wrist.
...possibly due to the stage of, or change of stage, in cognitive development. This is actually quite common, especially in childhood through the early teen years [where most people 'develop' LOL].
Or maybe you just decided it felt 'better' that way?
Perhaps they are one in the same?
There are people who cannot - not 'will not', but cannot wear a watch (or rings, bracelets, etc...) on the "other/wrong" hand/wrist. They cannot function. Most of us probably know people like this. I am not sure where I read about it, but there have been studies that show a 'mis-wear' can render some folks less than functional in addition to being uncomfortable. As I recall the study found that in most cases those who were 'single-sided' had either been that way forever or had been since some point in their life.
I guess sometimes what we think is a conscious decision - or even a fashion statement - could be a pre-programmed piece of code running at a low level in our brain we actually have very little control over, if any.