Does your wrist get sore or irritate?

Regular cleaning may help with the irritation. After an activity where I sweat a lot, I always give the back of the watch a quick wipe with some rubbing alcohol. I also occasionally clean the band in warm water with a bit of dish soap. I imagine the salt left over from your sweat will rub your skin and irritate it.

Also be sure you're not wearing it too tight all the time and that you let it dry out if it gets wet, as this can also cause irritation.

I'm not sure what difference it makes changing the wrist it's configured for.

Not an answer to your question about making a difference about the profile, left or right.  But I was having issues with irritation and it turned out to be the strap.  I have since changed to a fabric strap which solved my issue.

I haven't noticed any issues from not setting the wrist to right or left even though I swap it frequently. I have it set to the side I prefer and wear it on most, in my case the right wrist, and I wear it on my left at night. It still counts steps and such when on the opposite wrist.

I wouldn't bother changing your profile back and forth, but when doing an activity I'd use your primary arm so to speak.

You're supposed to set and wear your watch on your non dominant hand.  This way the watch doesn't mistake normal use of your domaint hand as starting to step or starting an auto activity. It makes sense in theory, but I've never tested it myself.