Cameron County Judge Carlos Cascos, who interviewed members of the Brownsville family with whom the toddler was staying, said they spent three nights in Houston just before he fell ill.
The hospital and health officials on Wednesday said the 23-month old boy had traveled from Mexico City to Brownsville, where he became sick and was medically transported to Texas Children's Hospital. They said he had had no outside contact. The family has shown no symptoms.
President Obama offered "my thoughts and prayers" to the family of a nearly boy who died in Houston, the first confirmed U.S. fatality among more than five dozen infections.
Texas called off all public high school athletic and academic competitions at least until May 11 due to the outbreak.
Schools are viewed as the perfect breeding ground for this flu, CBS News correspondent Bianca Solorzano reports.
Early Show medical correspondent Dr. Jennifer Ashton explained the raise in alert level, saying the shift is from "preparation to action."
"They're getting their sandbags ready for a flood," Ashton said.