TL;DR
When entering the US by land from Mexico, those under 18 years of age are exempt from testing and vaccination requirements.
The whole shebang:
This Travel.SE Community Wiki gathers the latest information about entry into the United States. After reciting that vaccination is required for entry, the page summarizes exemptions from those current vaccination requirements as follows:
The entry vaccine requirement does not apply to US citizens, US nationals, or lawful permanent residents (green card holders). The entry vaccine requirement does not apply to immigrant visa holders entering the US by air; however, a separate requirement as part of the existing medical exam requirement, means that new immigrants must also receive the COVID vaccine prior to receiving such a visa.
The following exceptions are permitted:
- air and sea crew members adhering to industry standards
- diplomats and foreign officials
- children under 18
- those who can't receive vaccines due to medical reasons
- participants in certain COVID-19 vaccine trials
- those in countries where COVID-19 vaccine availability is limited, seeking to enter the US on a nonimmigrant visa other than B-1/B-2 visitor visa
those granted exceptions by officials
US military members and their immediate family
Foreigners who are not fully vaccinated but allowed to enter the US due to the above exceptions must agree to comply with certain health precautions, and (with some exceptions) must agree to be vaccinated against COVID-19 in the US within 60 days of entry.
The Wiki cites several Department of Homeland Security webpages as authority for the Wiki's assertions. The easiest to follow is this one, which contains the following:
Updated Date: January 20, 2022
Beginning on January 22, 2022, DHS will require non-U.S. individuals seeking to enter the United States via land
ports of entry and ferry terminals at the U.S.-Mexico and > U.S.-Canada borders to be fully vaccinated for COVID-19 and provide related proof of vaccination, as COVID-19 cases
continue to rise nationwide.
These new restrictions will apply to non-U.S. individuals who are traveling for both essential and non-essential reasons. They will not apply to U.S. citizens, Lawful
Permanent Residents, or U.S. nationals.
...
Below is more information about what to know before you go, and answers to Frequently Asked Questions about cross- border travel.
...
Q: What are the requirements to enter the United States for children under the age of 18 who can't be vaccinated?
A: Children under 18 years of age will be excepted from the vaccination requirement at land and ferry POEs.
...
Neither the DHS statement (partially quoted above) nor the FAQ mention pre-entry testing. While one can't prove a negative, it's reasonable to conclude that "no mention" here means "no requirement."
Finally, remember that rules and regulations change frequently. This is true right now, but might not be correct next week...or even tomorrow.
