As you work on higher notes and enter the whistle register, notice a natural tendency to lift your chin and actively work against that tendency. It takes practice to retrain yourself, but it increases your power.
Practice breathing deeply and slowly releasing the air. Let the air out as slowly as possible to increase your endurance. Use this practice technique with a whistle note making it last as long as you can.
If you don’t have a vocal coach already, search one out who has worked with singers on their whistle register. If they have experience with it, they will be able to give you better advice.
To practice this, look at the lyrics to one of your favorite songs. Make a list of the phrases that contain words with these vowel sounds. Sing those lines entering your whistle register on the words with strong vowel sounds.
Take a break for a while and let your vocal cords rest. Never push past the point when you begin to hurt because you will end up damaging your vocal cords.