I thought the 'between' command only worked on DATE or DATETIME fields. Give that a shot, though.
Another solution would be to convert the date format in PHP, i.e. make the field in MySQL a datetime field and use:
$date = strtotime($dateFromCSVFile);
$date = date('Y-m-d G:i:s', $date);
Then insert the newly formatted $date into the database. This will allow you to use DATETIME fields, and then use syntax such as bough described.
As I said, I thought the 'BETWEEN' syntax only worked for date/datetime fields, though I've never messed with it. If it does, try using the code above (modifying it to fit the appropriate variables you used in your PHP script, of course).
Hope this reaches you in time! 🙁