There is no way that your handwriting will improve so quickly after just a few years of writing. Therefore, even if your handwriting is not very good, you do not need to worry about it now. However, if you really want to be able to write better than you do now, please follow this first. It may seem obvious, but you must write neatly.
You may think that even if you write neatly, something is still plain. However, if you always try to write neatly, your handwriting will surely become beautiful one day. Try it and see if you are fooled. It is true.
When you write, always try your best to write neatly. Once this becomes a habit, you will be fine.
No matter how word processors and computers become the norm, writing by hand will never disappear. You will have to live with your handwriting for the rest of your life. It is better to have a satisfactory handwriting anyway. To achieve this, it is important to be careful to write carefully and continue to do so patiently.
You may not see much effect in one or two years. However, writing is a lifelong process. There is a long way to go. If you write carefully, you will be able to write beautiful letters someday.