In theory, that stamp in your expired passport is still valid.
You're supposed to bring that expired passport and your current one and everything is supposed to be ok.
In actuality, I had a difficult time with American Airlines employees as I tried to check in when departing from the US all three times in 2013 and maybe the last time in 2012 (though not sure on this one), because AA employees didn't know what the original sticker was for. There wasn't a price on it that matched the current reciprocal fee, so they didn't know what to make of it.
After explaining that the ink didn't magically change to reflect the current reciprocal fee price, I usually had to go to Business/First Class check-in just to find an employee who knew anything.
Even with both passports in hand, you're going to have trouble with ignorant airline workers who are just protecting their own butts. ("Ignorant" does not mean "dumb", but they're not mutually exclusive either.)
I would contact your airline, tell them your situation, explain that you are supposed to bring both passports, and then see what they suggest.
Otherwise, you should contact the Argentine consulate in the US and see what they say.