I have a s3 and my wife had a s2. She got something similar from a Barton silicon band, which are great replacement bands, but apparently she can't use it.
Neither of us have a problem with the actually watch causing a reaction. Usually it is the band, which could be solved by a third party replacement.
I would use a healing lotion/cream on the cracked and dried area. Keep the watch off, or use it on the other wrist for a few days, while the irritation heals.
I would also use some diluted rubbing alcohol, like a lense wipe, to clean the watch of any odd residue that might be affecting your skin.
Then give it another try, and be sure to not over tighten the watch band (outside of fitness tracking usage). If the reaction comes back at the watch to skin contact point, you may need to return the watch (if it is possible).