She told me my range is D4-F5. My question is through continued training will I ever be able to sing higher notes, like up to C6,D6 or even E6
you've been at it for just a short time. Please be patient, and trust your teacher. The first thing is to get your "home" range in good working order, and then grow from there, both above and below. It is not uncommon for a mezzo-soprano to have a good c6 ( high c), and a d is not unheard of, although more in the category of stabilizing the c rather than as a usable note for itself. There are no plus points given ( nor taken away) for having these notes or not. What is more important is being comfortable with the voice you have,using it properly, and enjoying those realities rather than dreaming for something that may or may not be possible.
Also, age is a factor. A voice matures and ripens with the body. If a woman decides to have children, this will have a bearing on her voice afterward. ( Positive) The weight and richness also comes with age, so that a young or lyric voice may well ripen to a dramatic sound with time and experience.
A voice, well cared for, will last a lifetime, and should be considered a life's project.
Best wishes and keep on singing