You can pay a lot for a whistle and it still doesn't work. Loosen the head on your generation by holding the head in hot water until you can get it off, then cleaning the lacquer from the exposed end. You'll then be able to tune it.

When you're buying one, check that the airways are properly moulded, with the halves of the mould in good registration, i.e. no significant step around the inside of the fipple. Small amounts of moulding flash can be removed very carefully with a very sharp, pointed craft blade.

And don't forget that the breath control around the high notes is absolutely crucial for any whistle.