Dual citizenship international travel, US/POL?

I doubt it will even come up, although it might. just tell them exactly what you said here and that should settle it. tossing your US passport is an especially bad idea, since you need it to actually get in. if you don't have a US passport, you'd need a visa to go with your Polish passport and as an American, you can't get one. You'll just end up calling more attention to yourself and make them wonder just what game you're playing.