Three tear gas canisters shot from the US side landed around Meza and her children, who range in age from toddlers to teenagers, she said in an interview at a Tijuana migrant shelter.
"The first thing I did was grab my children," said Meza. A photo of her clutching the hands of twin five-year-old daughters Saira and Cheili, as her 13-year-old daughter Jamie runs alongside, has gone viral and sparked angry reactions from some lawmakers and charities.
"I was scared, and I thought I was going to die with them because of the gas," said Meza.
Her young son James nearly fainted when a canister landed near him. Meza fell and struggled to get up amidst the gas. A young man gave her his hand and pulled her to her feet.
"We never thought they were going to fire these bombs where there were children, because there were lots of children," said Meza, sitting in view of the rusted-steel US border fence.
"It wasn't right, they know we are human beings, the same as them," said Meza.
The US Department of Homeland Security said US Customs and Border Protection officers were struck by projectiles thrown by the migrants.
Around 5,200 people who travelled in a caravan across Mexico are packed into the shelter in a stadium in Tijuana, living in makeshift tents.
President Donald Trump has taken a hardline stance against the migrants, who have made their way north from violent and impoverished Central American countries. On Monday, he said Mexico should send them back to their home countries.
The US Border Patrol said most of those assembled at the border were economic migrants who would not qualify for asylum.
"I came here for one reason, and that's because there is a lot of violence in Honduras," said Meza, as her children played with empty tear gas canisters shot by the Border Patrol.
The United States shut the crossing for several hours on Sunday and Trump has threatened to close the border entirely.
"If they close the border I ask God that here in Tijuana, or in another country they open doors to us, to allow me to survive with my children," said Meza.
Maria Meza said she never expected the US Border Patrol to fire gas canister at children and families.