I have a Garmin watch/strap and I don't really know how the construction differs, but not only does the removable elastic strap get washed, but the receiver/transmitter part gets a scrub with a toothbrush now and then. The battery door is O-ring sealed, obviously, since it has to resist sweat and swimming, so it's fine to get it wet, and crud will build up in the strap that needs to be scrubbed off or it won't receive properly.

That said, I get a heat rash type of thing under my socks and sports bra. It doesn't really sound like yours - blotchy, red and raised, but not itchy or sensitive. I only get it in hot weather when I run over about 3 hours. Not on the bike no matter how long I ride or how hot the weather, not in cooler weather no matter how long I run, and though I wear different bras for running and riding, I sometimes wear the same socks. But it might be something like that?