odonme,
many immigrants (arabs, chinese, other europeans) from non-spanish speaking countries are in the same situation as you.
they just put their kids in school and in a matter of months they speak perfect spanish.
one of my workmates said his parents put him to school in an elementary school in the usa (he is a spaniard) when he was a kid, and he did not speak english but after a few months he just started speaking english. he is a perfect bilingual, i can’t detect a foreign accent, he speaks english like an american and spanish like a spaniard.
don’t worry about it. in two months he’ll speak spanish with a cordoban accent.