Today, I needed to come home early.

Today, I needed to come home early.

That is because national center test for university admissions will be performed at my university next two days.

I also took the exam to enter national universities.

I was 19 years old... I feel really nostalgic.

When I entered my university, I decided to grow into a competent adult in the future, but I haven't yet realized it.

In the meantime now, I have to post a paper to journal.

However, I can't go to my university because of the exam next two days, so I will study at home and sometimes play game for a change.

In fact, there is no TV and game hardware in my apartment now, so I'm mulling over buying new one.

(Actually, I wanted to play "The Legend of Zelda: Skyward Sword", but I lent my junior my TV and Wii 2 weeks ago...)

• Today, I needed to come home early.
• Today, I needed to come home early.

  "early"でもOKですし、イギリス系のネイティブは"ealier"をよく使っていました。こっちのほうが特別に早く～したというニュアンスが伝わるそうです。

• That is because national center test for university admissions will be performed at my university next two days.
• That is because the national center test for university admissions will be performed at my university next (or coming) two days.

• I also took the exam to enter national universities.
• This sentence is perfect! No correction needed!

• I was 19 years old...
• I was 19 years old...

  文末か文頭に"At that time" など時間を表す句をいれると文の前後関係がクリアになるかなと思いました。

• I feel really nostalgic.
• I feel really nostalgic.

  これはテストについて述べているのすか？もしそうならば、”I feel nervous " などが語句として適切です。全文が過去ですので、felt に変える方が自然です。

• When I entered my university, I decided to grow into a competent adult in the future, but I haven't yet realized it.
• When I entered my university, I decided to grow into a competent adult in my future, but I haven't yet successeed it.

  まだ実現できていない意味で、successをあてました。

• In the meantime now, I have to post a paper to journal.
• In the meantime now, I have to post a paper to journal.

  "Meantime"は現在の状況に付け加えて何かを述べる時の表現ですので、nowなど時制はないほうが自然です。

• However, I can't go to my university because of the exam next two days, so I will study at home and sometimes play game for a change.
• This sentence is perfect! No correction needed!

• (Actually, I wanted to play "The Legend of Zelda: Skyward Sword", but I lent my junior my TV and Wii 2 weeks ago...)
• (Actually, I wanted to play "The Legend of Zelda: Skyward Sword", but I lent my junior, my TV and Wii 2 weeks ago...)

• When I entered my university, I decided to grow into a competent adult in the future, but I haven't yet realized it.
• When I entered my university, I decided to grow into a competent adult (or: person) in the future, but I haven't yet achieved it. (or: haven't achieved it yet)