Hi
It is possible that you have only scratched through the fingerprint-resistant, oil repellent coating. It is normal for this coating to wear away under normal use, but it may have become scratched without damaging the screen beneath.
Unless the issue is due to a manufacturing defect, cosmetic damage - including scratches - is not covered under either Apple's Limited Warranty or AppleCare+.
Apple does not offer a screen repair or replacement service for Apple Watch and Apple Watch is not user-serviceable. Your watch may instead be eligible for chargeable, out-of-warranty service.
I suggest that you contact Apple Support (mail-in service may be available), make a Genius Bar reservation or visit an Apple Authorised Service Provider with a view to having your watch inspected and to establish any available service options, likely timescales and cost:
Note that, whether you have scratched the screen or not, note that Apple does not recommend using cleaning products or polishing or buffing the watch with abrasives; these will wear away the coating and may also (further) scratch the display.
A good quality screen protector (of the thin film type) may be effective in obscuring or reducing the visibility of the mark, as well as in providing some measure of protection against future damage.