Every singer who has ever gotten voice lessons deals with this. Do not be upset if it takes considerable time and practice for you to learn how to sing the high notes freely and easily.
If you keep practicing regularly and carefully, you will get better at it over time. There are certain techniques you can practice to make the high notes sound better, but it all comes down to consistent practice and help from your teacher to overcome problems when you get stuck.
Your vocal tract contains many small muscles, most of which you aren't conscious of using when you sing. The more you sing, the more you learn how to be aware of them and control them. As you do this, you can expand your range and improve your tone and your phrasing. Singing is a sort of an athletic endeavor, on a very subtle scale. You can build up strength in your vocal tract, or fatigue or injure it if you are not careful.
There are some different theories as to how to go about improving the high notes. Sometimes we refer to these as ideas about "voice placement". You just have to find out what works best for you. Your teacher can help you become aware of the position of your larynx and soft palate, and how to control them, for instance, as you form each note, and of how to modify the vowel sounds of high notes to make them easier to sing and to resonate better.
I'm a tenor soloist, and I studied voice at university. Almost 25 years ago when I was about to leave college, I sang a solo in front of all the students of my voice teacher, and in this solo I hit a high B-flat. A young man who had just enrolled in the school as a first-year student came up to me and said, "How can you sing those high notes and make them sound so good?"
I looked at him and said, "You practice every day for three or four years."
Even if you learn good techniques, you have to patiently practice them to get results.