The simpliest way to do that is use an array to store already added values and check for duplicates.
if((($handle = fopen($fajl, 'r')) !== false)) {
$stored = [];
while(($data = fgetcsv($handle,1000, ',')) !== false) {
//skip current row if it is a duplicate
if (in_array($data[0], $stored)) { continue;}
$sql = "INSERT INTO csvtrenutna (brpolise, iznos) VALUES('".$data[0]."', '".$data[1]."')";
pg_query($konekcija, $sql);
//remember inserted value
$stored[] = $data[0];
}
}