I think that you might need to reassess your embouchure. When playing, try to pay attention to the shape of your mouth and the direction of your airflow. Lower notes should have a steeper, downward direction and your mouth should be in the shape of an oval. The corners of your mouth should be directed down like a frown. For higher notes, your breath should still be directed downwards, but try stretching out your upper lip a bit more. This could give your airflow more strength. Your mouth doesn't need an ovular shape for higher notes, but more round.
I think that the best way to fix issues like yours is to go back to the basics and work on your technique. It may be frustrating in the beginning, but mastering the simple techniques is the key to mastering the more difficult ones later. The further you go along with the flute, the more challenging the pieces you play will become. Try to fix your technique earlier on so that you don't develop bad habits in your later playing.
To practice your embouchure and tone quality, play two-octave scales by holding out each note, and pay special attention to your embouchure and sound quality. You need to develop better tone, so play around with it on each note. Experiment with your embouchure, and take note of what sounds better for each note. You should notice that you'll need to change your embouchure when moving from lower to higher, and then higher to lower notes. Once you feel like you've had enough of scales, try practicing simple pieces. Don't be afraid to stop and hold out a note that you have trouble with, or to slow down the tempo to work on your tone quality and technique. A metronome could really help you out here.