for some reason
Not necessary
I made it as my life mission to do random acts of kindness whenever I can.
I vowed to perform random acts of kindness where ever I could.
I was very determined to make other people smile.
You still are determined! "I have always been determined to make others smile"
Unfortunately, not everyone thinks in the same way I did
Unfortunately, not everyone shares my beliefs.
they do drive me up the wall
This metaphor is overused. You should just say that they get to you or hurt you.
it does not mean that they are the bad people here
but they are not bad people
the never-ending rat race
To what "rat race" are you referring? You need to be specific when mentioning things like rat races. Furthermore, "rat race" is another stale cliche. It would be better to simply state a specific difficulty that people are facing.
suspicious to nice strangers -and any strangers at that too.
suspicious of strangers--even nice ones
That is why I think random acts of kindness are really important.
What is why? Your prior sentence does not explain why kindness is important. You can get rid of this sentence, because you explain at the beginning your inspiration for sharing kindness.
These selfless acts are not only capable of bringing joy to the recipients but also to the givers.
This is an interesting idea. You could explain it a bit more.
I want to show the people how the little things they give could make a big difference in someone else's life.
How would you show this? Do you have a specific example? You need evidence to back this up.
it is possible for us to live in a world where we can share all the happiness in the world without the worries of paranoia between us
it is possible for us to share happiness and forget paranoia
Hopefully, when that day comes, I will still be alive to experience it.
This is unnecessary. I think it is very obvious that you want to see this happen; you don't need to overemphasize this idea.
and maybe, along the way, I will get to meet that same boy I met 13 years ago.
You should not say this. It sounds immature.
Overall, this essay is very sweet. You share some lovely ideas. However, this essay could benefit from some organization. Paragraphs wouldn't hurt. Furthermore, you need to provide evidence (in the form of personal examples, specific anecdotes, etc) for your claims. For example, when you say that people are suspicious, describe a SPECIFIC time in which your actions went unappreciated.
Good luck!
(Could you please edit one of my essays? Thanks!)