The Covid travel rules for Americans entering Jamaica has not changed.
The Covid travel rules for exiting Jamaica HAVE changed.

Please read thoroughly and provide required information at...
https://vistjamaica.com.
A negative antigen test is required for entry into Jamaica.

Covid entry requirements into the USA now include One Day Antigen testing with negative results before your flight. This Dec.6th, 2021.

Jamaica is well versed in providing these tests and this should cost around $50us each.
Your hotel can help you arrange for testing.
Or, you can find testing locations across from Coco La Palm, at IDoc located at the Boardwalk Shopping Village and there's also a testing site located on the sidewalk almost across from the Beach House Villas.
There are other locations...they're very easy to find.