Is it really necessary to have the thesis even though I've been told the other paragraphs convey the message well?
Well, the thing is, advice you get from me reflects my philosophy of writing. For beginning writers, it is important to take advice from someone like me so that they are not in the dark, but for you it is okay to use your own approach. You don't have to do it my way; I just tell you about my way to give you a different perspective.
But this is to sharpen the specificity of a sentence: ...
I was preoccupied, because it wasAnd this is to sharpen the specificity of the whole essay:
a sentence that sums up the main message of the essay, right here at the end of the first paragraphSo, my logic is about sharpening a piece of communication. If you sum up the message in a sentence at the end of the first para, it sharpens the communication.
But what does it mean to sharpen communication?
Anyway, the bottom line is that it is not necessary, just an idea. And if it would put you over the word count, it really is better to cut a sentence to make room.
Making Room
Actually, all your sentences are good and necessary, so you can't cut any! You would have to
combine the last two sentences of the essay and make them more concise, and also make more room by making this part more concise:
My degree of uniqueness was, at first, limited until I told everyone that I found the program myself. Everyone else was recommended by a teacher but I wasn't.