Rash from Apple watch

See the 'For people who are sensitive to certain materials' and 'What's in the bands' sections of:

Wearing your Apple Watch - Apple Support

It would appear the watch is not your issue, but the watch band is. Which band are you wearing? You didn't post a photo of the side of your wrist the watch itself sits on.

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We want to make sure you reach the right team for help with your device. We recommend that you contact Apple Support directly. Depending on your region, you may be able to reach them here: Get Support