A few points to remember about expanding your vocal abilities are as follows.
Before you work on extreme methods of singing high notes, be sure you understand the basics of vocal production. This is absolutely necessary. Your voice can be damaged if you do not comprehend how it works to begin with. You know how a hoarse voice feels if you scream at a baseball game one day and can hardly talk the next.
Vocal ranges are defined as soprano, alto, tenor and bass. SATB is the acronym which refers to the vocal ranges. Your range is defined as the lowest note you can sing pleasantly most of the time to the highest. Your teacher can help you define what your range is or you can go up from middle C until you can no longer comfortably go and downward in the same way. You can refine your range only when you know what it is.
In order that you do not set yourself up for failure, set an achievable goal. If you want to be reasonable, do not set a goal of reaching an extra octave of range in the near future. You may incur lasting injury to your vocal cords if you choose such a goal. Practice and diligence are the only things that will bring results. Always warm up your voice before attempting to stretch it, just like a runner. Warming up is done by all singers and with good reason.
Your voice will become better with time and practice. Runners and singers must follow the same rules in this regard.
Always get guidance from an instructor or program in order to improve. Teacher to student is the best way, albeit expensive. Many online programs offer a perfectly acceptable alternative to the teacher and student relationship.
While you practice your singing at home, try these two ideas.
Exercise standing, facing a mirror. In this way you can observe the position of your jaw and chest. Your posture should be correct and your jaw should not reach up for the high note. It is a natural inclination to reach with your posture, but this harms your ability to hit the note.
None of us hear ourselves the way we actually sound, record yourself and see. It is a shock at first to hear what you sound like, but if you continue to use this valuable tool you will get better even quicker. If you record a lesson you can go over and over it to pick it apart, so to speak. Money for lessons is not easy to come by, get the most out of your lessons.
In the state-of-the-art study of singing, time and effort will produce the best results if you want to become a better singer.