If you are feeling the watch is hot on your wrist (or generally hot to touch) a genuine heat burn is possible, but relatively unlikely because the watch battery is only small and does not really have enough power to make the watch hot for long enough to cause burning. You would certainly notice if this was happening, because making the watch hot would discharge the battery fairly quickly and you would be complaining about battery life.
It is more likely you have become sensitive to something in the watch or watch band, or possibly some kind if irritant like a soap or detergent trapped under the watch and not easily rinsed away. Take a look at this support document, and if you are unsure then consult your doctors who can look at the relevant arm with their own eyes.
Wearing your Apple Watch - Apple Support