I get an "iPhone out of date" messe\age when trying to pair my new Apple watch...I updated my phone (6Plus) so the iOS is 12.4.4

You cannot pair a current shipping Apple Watch Series 3 or 5 with an iPhone 6 or older.

Apple Holiday Return Policy (Purchase between: 15-Nov-2019 thru 25-Dec-2019, Return by 8-Jan-2020)

All purchases made before November 15, 2019 and after December 25, 2019, are subject to the Standard 14-day Return Policy. 

https://www.apple.com/shop/help/returns_refund

The current shipping Apple Watches require an iPhone 6s, SE, 7 or newer running iOS 13. The iPhone 6 cannot upgrade to iOS 13.

A new apple watch 3 or 5 will NOT pair with an iphone 6 or lower,a new apple watch 3 and 5 have software version watchos6 on them,this requires an iphone with ios13 or higher on them.Iphones with ios13 are an iphone 6s, or higher.Iphone 6 can only update to ios12 maximum.

You have 14 days to return the watch for a full refund.