Others have posted about this with other Apple watch bands. In some cases, the symptoms almost seem like carpal tunnel syndrome (CPS), in others, something different.
If CPS, it could result from frequent turning of wrist in order to check things on the watch (another reader pointed this out recently in a different thread). That is a repetitive motion issue, could result in sharp pains and even numbness sometimes near but sometimes not near the watch itself. Not sure how to address that other than to suggest not turning the arm/wrist as much when checking the watch, or checking it less often. To diagnose CPS one needs to see a medical professional, worth doing as it can be serious due to nerve irritation and even potential nerve damage.
If the pain is simply due to the band itself, you can try other bands, maybe ones with more "give" or stretch. Or try loosening the band as much as you can without compromising ability to detect heart rate, oxygen sensor, etc.
Others have reported some skin irritation from friction of the watch band, but that does not seem to match what you have. When that happens one can usually see some visible irritation on the skin. I had a little of that when my Series 11 watch was new, it went away when I loosened the band one notch. I have the simple rubber sports band.