You could have worked hard and your range substantially extended to sing those higher notes, however you are struggling to sustain them. Or your voice becomes very easily fatigued when singing a piece that contains a lot of high notes (unlike the normal way of hitting one high note and returning down).
If you are in any of those circumstances, range is not your issue: it's "tessitura". Tessitura is your comfortable range, in which you can sing the notes consistently, on-pitch, and without strain. The term is usually used to describe the average pitch range of a song or choral part.
For instance, a number of mezzo-sopranos are able to sing an occasional high C at the extreme of their range. However their tessitura is probably an octave to half an octave below that: maybe from the A above middle C to the second A above middle C. They are going to experience vocal strain and fatigue if they tried to sing a song where the tessitura is from high G to high C.
The key to select songs within your range is to know where your tessitura is. You may be in danger of straining, and eventually damaging your voice should you sing beyond your natural tessitura for very long periods
So, can you really improve your tessitura? It will need lots of effort, but yes it is possible The main factor is breath support, along with upper resonance. You're going to get vocal strain if you attempt to sing high without supporting those notes with adequate breath support. Over a long period of time, you might result in long-term damage.
To sing higher you will need more breath energy than singing notes which are lower. You need to use all your breath muscles-diaphragm, abdominals, spinals, and intercostals--and completely expand your midsection with each inhalation. When you exhale, keep everything expanded with the exception of your abdominals, which will regulate the rate of breath flow.
Once you're breathing properly, focus on your upper resonance, or "head voice". Imagine the tone to be vertical rather than horizontal, and think of the sound coming from your forehead and the top of your head. Imagine your breath as being the mechanism which makes an elevator ascend, and it is riding up to the top of your head
You ought to feel the vibration inside your sinuses as well as the roof of your mouth (soft palate). Keep your mouth horizontally narrow but vertically tall inside. One particular vocal instructor explains her students to imagine trying to swallow something unpleasant, opening the throat enough so that whatever it is will not touch the sides.
Keep your tone light; do not try to force anything. Start with the yawn-slide or the vocal siren. For the yawn-slide, breathe in and open your mouth as if to yawn, then exhale on "hoo" or "hee", starting at the top of your range and sliding quickly all the way to the bottom. Try to start each successive one a little bit higher.
The vocal siren is similar, with the exception that it starts at the bottom of your range and goes up. Do it using a hum. As your breath support becomes stronger, perform the siren down and up many times on the same breath.
Another good workout is the rapidly ascending and descending five-tone scale. Begin in the middle of your range and use either the buzz (also known as lip roll or bubble lips) or a vowel sound, such as "oo" or "ah". The routine is do-re-mi-fa-so-fa-mi-re-do. Begin the next sequence a half-step above the first and continue in that manner. Make sure to use good breath support.
With dedication, you'll be able to increase your tessitura and sing higher notes a lot more easily and comfortably. You should be patient, persistent, and realistic.