Same happened to me.
I have come to the conclusion that this is due to the intensity of the green lights at the rear of the watch. It's basically a form of sunburn but not caused by the sun obviously. I have written to Apple and asked that they display this prominently on the documentation for the Watch.
Since any kind of light based burn puts you immediately in mind of skin cancer it's quite concerning.
When I called support they made more fuss about it being a nickel allergy .. which it clearly isn't - I wear other watches (in fact I wear more than 1 at a time, and they are made of steel and I've had no problems). I don't think Apple want people to dwell too much on it being based on the intensity of the light on the rear.
If you like your Apple watch, as I do for its other features.. you can of course turn off the heart monitoring (its under settings / privacy / health), and it no longer burns. They need to stop vacillating on this and come clean.
Apple also make suggestions around the tightness of the band.. this is because (i think) that the natural movement of the watch spreads out the dosage any one area gets. But that isn't really a solution.. because the documentation also says that for the ECG to work the watch must be "snug"
- "Make sure that your Apple Watch isn't loose on your wrist. The band should be snug and the back of your Apple Watch needs to be touching your wrist."
So they want it loose, but snug...