Okay, so first, a few clarifications.

I know that Choctaw and Chickasaw came partly from Mexico or Central America

I am not familiar with this assertion. You may have been thinking of the Choctaw/Chickasaw origin story, which describes an eastward migration from lands to the west of the Mississippi River. As far as I’m aware, no definite origin point for this migration has been determined by the Choctaw/Chickasaw or by scholars, and the only direction given is west, which would in all probability still place the Choctaw origin somewhere within the modern United States (I have heard interpretations claiming the Pacific Ocean, which is a remarkable journey, but it isn’t Mexico nor is it Mesoamerican).

Modern scholarship tends to assert that the Choctaw, as a contemporary ethnic group, came into being in the 17th and 18th centuries as a coalescence of various southeastern groups in response to European colonial pressures, among other things. A similar process seems to have occurred for the Chickasaw (though the ethnic identity of “Chickasaw” can be traced back to at least the 1540s, as the Hernando de Soto expedition stopped at “Chicaza”. That being said the Chickasaw definitely amalgamated several other groups in the period between 1540 and the present). This places the ancestors of the Choctaw and Chickasaw as having deep roots in the US southeast, as direct descendants of the Mississippian and earlier moundbuilders. Notably, this would align with the other Choctaw origin story, that they emerged from the earth at Nanih Waiya, a mound in what is today central Mississippi. It’s possible, even likely, that a group migrating from the west may have joined with these long-rooted southeastern residents to form the modern Choctaw.

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