I twisted the strap/monitor portion around to my left side for my ride today and no problems. Marni probably nailed it with her suggestion that perhaps my usual washing treatment isn't getting all of the salt out. The strap goes in the washing machine every two weeks and gets rinsed after every use but that doesn't mean all of the salt/perspiration is getting removed. Hard to see how not...but something is causing this and that is the easiest explanation.

The contacts don't touch my skin so I can't see how it is some new allergic reaction. I appreciate the comments!