Hola Sara, I hope all works out well for you!!!!

I had a similar situation, but was told by the Ezeiza guys that I had to pay a fine if I wanted to leave the country with my US passport, after having entered it with my Arg. one. My Arg. passport had expired in the meantime... I think the fine was like U$30. This was back in late December. I ended up not leaving because there was a passport problem with a relative of mine.
However, they never told me I could not leave the country...
Since then, I have renewed my Arg. passport... yes, long lines!... and, yes, if you do go to Azopardo, go there with A LOT OF PATIENCE AND A GREAT BOOK TO READ, or a good friend to chat to...!

Looking forward to seeing you soon!