However, feeling much better today, I made up my mindecided to open the book again.

What you had wasn't wrong, but "made up my mind" sounds like you couldn't figure out what to do. "Decided" sounds more like a concrete choice. Also, "However, feeling much better today" is perfectly correct, but a more conversational option is "Now that I feel much better today."

I wanted to study in a cafe, but since today wais Boxing Day, most of the places weare closed or open later.

"Today is Boxing Day" uses is since it is current, and "most places are closed" must still use the present "are" since the places are still currently closed. Saying they "were closed" implies that it's no longer Boxing Day.

As the same asJust like yesterday, I started my day by cleaning my home and sat at my desk to open the Grammar book.

Maybe it's just me, but "As the same as yesterday" sounds a bit choppy. "Just like yesterday" is one of many smoother transitions.

I played thea Pomodoro method video from YouTube and read sentences out loudly.

"Loudly" is about volume, but "out loud" is about saying it with your voice (which is what you did). Also, say "a Pomodoro method video" because there are hundreds online, and you chose one (unless there is a specific one you chose). In that case, if you want to say "the," you could say "I played the Pomodoro method video that I always play" or something like that.

This book is composed of 113 units, so there are 14 more units left.

Perfect sentence! A very common pitfall that you could have made (but didn't) is saying "This book is comprised of 113 units." Saying "comprised of" when you're supposed to say "composed OF" is a very common mistake among native English speakers. So you know the difference, using comprised requires you to say, "The book comprises 113 units."

I will finish the remaining units and take the quizzes in this book to check my understanding.

Need "the" article

I wanted to study in a cafe, but since today was Boxing Day, most of the places were closed or opened later.

Minor point that I'm not sure matters, but I feel like this is slightly more natural to my ears.

AsJust the same as yesterday, I started my day by cleaning my home and then sat at my desk to open the Ggrammar book.

Adding "then" gives a stronger sense of a timeline of events.
"grammar" does not seem like a proper noun in this case, so doesn't need capitalising.

I played the Pomodoro method video from YouTube and read sentences loudly.

If there is one specific "Pomodoro method video" that you have already discussed or expect your audience to already be familiar with then referring to it with the definite article "the" is correct. But if the audience would not be able to tell which video you mean (ie: there's multiple and it's unclear to which you refer to) then "a" would be more appropriate.

This book is composed of 113 units, so there are only 14 more units left.

Minor suggestion to emphasise how you feel that it is only a few units left.

I will finish the remaining units and take the quizzes in this book to check my understanding.

This is a case where the definite article makes sense, since this could only refer to one thing.