It was a little past one o'clock at night when I woke up because I felt like peeing.

"Pee" as a verb is an informal word. For more formal writing, you can also use: "use the toilet", "go to the toilet", "urinate". ("Urinate" isn't really used in conversations, but the other two quite commonly are.)

I couldn't fall asleep again.

Alternatively: "I couldn't fall back asleep."

I tried to write out some of my thoughts in English and record this caseincident.

Alternatively, just for your information: "I tried to pen down some of my thoughts".

If I can't, I'm worried about themy performance I'll do tomorrow.

In the phrase "do a performance", "performance" refers an act like a play or concert.

Hopefully, I will fall asleep soon and I will be as energetic as I was duringon those days when I had a good sleep.

You can omit the second "I will", as it is redundant.