I really liked you choice of topic, mainly because it's unique. However, to be frank, the thought process doesn't flow very well. I would have to reread some of your sentences several times before I understand what they means in relation to each other.
However, one value stood out most from all the others
The other what? Other communities? Other values? You were talking about how distinct the communities was from one another, and then you suddenly switched gears.
people are beginning to get more and more caught up with the little things in life
Such as?
It's even becoming a society norm
What became a society norm specifically?
But what makes us human? Care
How?
It can change our communities and even peoples overall growth
Again, how?
I was the girl who only cared about the little things in life.
Some example of your personal examples would be good
but as I grew older she was right
Did you had some sort of experience that proves that your grandmother was right?
the world has more to offer when you put more concern into yourself, the people around you, and the environment
I see your concern for the environment and for other people. But where is the concern for yourself?
When we care for our environment and the city, people all around us benefit. Recycling or simply not littering can help benefit our local communities in a multiple of ways.
What benefits? Also why did you list specific examples such as "recycling" and "not littering" for environmental care, but you didn't list specific examples for "concern for yourself" and "for other people." "Doing a good deed" is broad and not specific. Did you gave out food to the homeless? etc.
It doesn't necessarily mean the world needs to be eco friendly or be the next Gandhi for a positive change. But the simplest acts of caring can make a huge impact in different aspects.
Personally, I feel that this can be simplified and combined as one sentence. I would stay away from an ending sentence that start with "But", unless there's some type of dramatic effects, which I don't see any here. Also, "different aspects" of what? Of the world? of Life?
I think it might be better if you includes some examples of how the value of caring affect you personally. Not just that it does, but how? Your mental development, maturity...Maybe include something that you saw while on the move from place to place?
Overall this is a good essay. You just need to use more and better transitions as well as concrete examples.
That's all for me, sorry if I offended you. Hopes this helps :)