‘We became like a chicken in a cage,’ a migrant says, trapped between Belarus and Poland.

Exhausted, freezing and exposed to the elements, Bayar Awat, his wife and infant daughter have been stuck on the Belarusian side of the Polish border for more than a week after leaving their homes in a desperate gambit to reach the European Union.

One of several thousand migrants from Iraq’s Kurdistan region at the Belarus border, Mr. Awat said that he knew Belarus was using migrants like him and his family as pawns in its own political battles, but that he was determined not to return to Iraq. He and...