Wow, I really liked your essay. It's simple, sweet, and successfully conveyed the point.
First off, try to used paragraph. Having an organized structure really helps the audience, even if the topic is simple.
I liked your points, but it would be more convincing if you could back up everything point about your mother with some examples. How did she motivate you? What did lessons did she taught you?
Try not to begin a sentence with "My mother" too much.
Try to emphasize and expand more on what your mother inspired you to be, and have specific examples of how you are going to keep your promise to her.
So, I just make one silent promise to me and to my mother; that I will get my education and be the best I can be and when I reach a point where I feel like giving up I will just think about my mom and how she never gave up and. That will be the push that I will need to be that successful teacher and able to take care of my mom liked she took care of me.
This is a run-on. Try splitting it up into multiple sentences.
Overall good essay, just try to avoid repetition and try to separate it into a certain organizational pattern via paragraphs.
Hope this helps :)