In a post apocalyptic Mexico, a pregnant teen risks her life to cross the closed border so her son can be born an American citizen.

Totally agree with Adam. That would make a very compelling premise.

A great idea, a unique twist: reverse the situation. People are desperately trying to flee a post-apocalyptic U.S.

I'm with dpg on this. People are crossing the border now for this very reason, and some right wing extremist groups are going to great lengths to prevent them, by building walls and having militia groups patrolling the border.

In a post-apocalyptic world I don't see how it would even matter where the baby is born, since everywhere would be just as bad. Also, there would quite possibly no longer be any governments and all borders would be meaningless.

One thing that COULD make it an interesting reason to set it in a post-apocalyptic future is if ? provided that there still were nations and borders ? the situation was reversed from now and the US was maybe a bit worse off than other places and people were desperately trying to get OUT of there, including the mother who instead wants the baby to be born in Mexico instead. If you flip the situation, then it might be a reason to place it in the future, otherwise you could just set it in the present.