There are a few triggers for your skin changes under your watch...
The first is moisture and soap residue build up between the watch and the skin. This is the most common issue. Often people come in worried they are allergic to their wedding jewelry (and worry their spouses bought them the ‘fake stuff’:). The real issue is that if water and soap build up between a watch or other jewelry item and the skin, the result will be the beginnings of skin breakdown. Essentially the soap starts to do its job and emulsify the fats and lipids in the superficial layers of skin. This turns the skin white and macerated and appears ‘wrinkly’. If the skin is not addressed at this point then dead skin cells start to accumulate and the keratin can start to smell (kinda like the cheesy white stuff that comes out of a cyst or a pimple).
The second issue that comes up is that some are allergic to the nickel and rubber in the watch backing and bands. This would present a little different however. Initially it would appear as a red itchy rash as opposed to skin wrinkling and breakdown.
For the first scenario, it’s a good idea to dry the skin completely underneath the band and watch face after washing, sweating or showers to avoid moisture buildup.
For the second scenario, finding a barrier option to place between the watch and the skin or coating the metal with a sealant if possible may help.