Now I am now a full time worker and a college student.

Putting "Now" at the start of the sentence can come off as pretty forceful or attention grabbing. It's fine in the first sentence, but doing it multiple sentences in a row comes across a bit strong.

I wake up at 6:20am, eat my breakfast, and get ready to work.

I start my work at 8am and have lunch break at 12apm.

12am is midnight, 12pm is noon.

I go back to my house at 5pm and have a shower.

These days, in my free time, I play Ts4 (The Sims 4?).

I always liked this game, but my notebook couldn't "play" (?)/run it.

"play" is fine, it can sound a little casual when you're talking about the computer doing it rather than the person, "run" is a little more general purpose.

I'm so happy ofabout that.

Oh, and I was reading Flowers for Algernon (which I liked sm), but now I don't have much time to read tooeither.

"either" is used more often than "too" in a negative context.

First time being an adult,; kinda nervous

Now I am a full time worker and a college student.

I wake up at 6:20am, eat my breakfast, and get ready to work.

I start my work at 8am and have a lunch break at 12apm.

I go back to my house at 5pm and have a shower.

I study, and then go to sleep.

These days, in my free time, I play The Sims 4 (Ts4).

I always liked this game, but my notebook couldn't "play" (? it (or run it).

I'm so happy ofabout that.

Oh, and I was reading Flowers for Algernon (which I liked sm), but now I don't have much time to read too(in addition to everything else).

I'm not sure what "sm" is

I wake up at 6:20am, eat my breakfast, and get ready to work.

I start my work at 8am and have a lunch break at 12am.

I go back to my house at 5pm and have a shower.

I've always liked this game, but my notebook couldn't "play" (?).

I'm not sure what you're trying to say here. Sorry, I don't really know anything about tech or gaming.

I'm so happy of that.

Here are two possible sentences that are more natural:
That makes me so happy.
I'm so happy about that.