Today, I wore a pink shirt with athe quote "DIALOGUE WITH AHTLEB".ialogue with Ahtleb."

Any quote that exists: a quote
A specific quote (e.g., the one you are about to mention): the quote
Punctuation (periods) go inside ending quotation marks

To be honest that , I don't know what that means.

I cleaned my type ofstyled my hair like athe handsome guy I am.

Making our hair look nice = styling our hair.
I changed the end a bit to sound like a natural phrase; it is a little cute way to say you look handsome without sounding too arrogant

I'm pretty sure that it makes me look fresh/cool.

Alternative to "I'm pretty sure that it..." is "I feel like it..." which would be slightly more optimal here, as it is used for more subjective things.
"Fresh" isn't used very often in slang; I would just go for the standard "cool" or even "stylish"

Now I'm (gonna/going to) go to the beach near the Shinan district using my fishing reel to catch some fish.

Obligatory mention here that "gonna" is not considered as correct English, and "going to" is. But in every day life, we do say it often. Just keep it in mind for when you are doing professional communications.

Let's sStick with me.

Stick with me = you are telling us, your readers, to stick with you.
Let's stick together = you are now speaking for all of us, yourself and your readers, to stick together.
Both options here are fine.