Hello, this is not an Apple Watch issue. I do not own any Apple products, but came looking for "Apple Watch Wrist Burn" and landed here, because my Garmin watches have done the same thing three times. Replacement of the watch doesn't really help. Like other respondents here, the issue may not arise for a long time, or it may come back after a short while or a long while. Every sports watch with wrist sensors I have investigated has this same problem.
A dermatologist may not be able to tell you more than that you have contact dermatitis. There doesn't seem to be a solution, despite all the manufacturers being aware of the problem.
Advice from multiple sources says to scrupulously clean the sensors and get them completely dry before putting the watch back on (a completely dry) wrist. Don't use perfumed, scented soaps or moisturizers on the wrist. Don't leave the watch on if you are going to have a wet wrist (kind of difficult if you run and sweat...the idea is to remove the watch as soon as possible after a sweaty session).
The basic advice is to keep the back of the watch clean.... There are myriad articles online like this linked one suggesting what to do: https://gadgetsandwearables.com/2023/01/24/fitness-tracker-rash/
I hope this helps. This is a very frustrating problem for all wrist sensor wearers...you never know if you're going to have it happen to you.
I won't be back to reply to comments...as I said, I'm not an Appleite. Good luck/