네, 화이팅 ^^
 

YeHeT23 has given you good corrections already, so I will just comment on some colloquial English language suggestions (that is, English that English native speakers would use in daily language).
 

"I got a hangover when I woke up" --> "I had a hangover when I woke up"
 

"I got drunken" --> "I got drunk"
+ you do not need to add "en" to this adjective (drunk) ^^
 

"I had taken a shower and got out of my home without having a breakfast" --> "I took a shower and left my home without having breakfast"
+ "had taken" is grammar you use only when you tell a story in the past tense, and then you want to talk about something that happened BEFORE that past tense. For example: "Before I left home, I had taken a shower." In this sentence, "before I left" is already past, and "I had taken a shower" is BEFORE that past. You only use "had + verb(en)" when something happened before past tense.

(this is confusing, even to native English speakers!)

 

"I have feeling sick during on my way to work" --> "I felt sick on my way to work"

+ "have feeling" is okay, but "to feel" is the verb form that you can use by itself. If you want to use "have feeling," change "have" to "had" because your notebook is in past tense. 

   + you also have to use "had a sick feeling" because "sick" describes "feeling." Word order in English: adjective-noun.

+ "during" and "on" : use "during" while you talk about specific activities. "During my bus ride to work," for example. "Bus ride" is the specific activity. "On my way" is a colloquial phrase and you do not need to add anything to it in order to indicate time.

"Fortunately, I passed away my work time without any trouble" --> "Fortunately, I passed the time at work without any trouble."

+ YeHeT23 already said this, but "to pass away" means "to die" in English, but it is a softer term than "to die." You use "pass away" when you want to be delicate or polite. 
+ "To pass the time" is a phrase that you can use instead. It's like "시간을 보내다."

"After an hours" --> "After a few hours" or "In a few hours"

+ the word "an" can only describe a singular noun^^ You can say "after an HOUR" but you cannot say "after an hours."

     + You can describe "hours" with "a few" so that you can use "an," but "an" has to change to "a" because "hours" starts with a vowel sound. "After a few hours." 

+ Because "after an hours" is going to be in the future, you can say "in a few hours" to mean the same thing. "A few hours from right now" means the same as "in a few hours."

"weather of tomorrow" --> "tomorrow's weather"

+ "weather of tomorrow" is completely grammatically correct. However, an English speaker would say "tomorrow's weather" instead. The " 's " indicates possessive like "의" in some sentences in 한국어. For example, this phrase: 여지의 가방 in English is "the lady's bag" or "the bag of the lady"

Good job, 정훈 ^^ Please keep working hard!!

My ordinary day : )

Hi, my name is Jeong Hoon Lee from South Korea. This is my first notebook : ) so, from now on i`m about to write just diary of today. Now I will write today's diary.

I really didn't want to wake up early this morning but i I had to go to work. I got had a hangover when I woke up because I got drunken drunk with my seniors and friends at last night. I had taken took a shower and got out of left my home without having a breakfast. As soon as I got out of my left home, i I felt terrible, because it was freezing outside. Furthermore, I have feeling felt sick during on my way to work. I was eager to have hangover stew.

Fortunately, I passed away** finished my work time time at work without any trouble : ) After an hours, I can go to my home! As soon as I get home I will take a shower and have a conversation with my girlfriend on the phone. I hope that the weather of tomorrow will be nice. 

Thanks for reading my notebook! Have a nice day everybody : )

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Please stay warm! I hope the weather is nicer for you tomorrow. :)

**Like YeHeT23 said, to "pass away" means "to die". It is a nice way of saying that someone has died. For example, it is more respectful or polite to say "he passed away in his sleep" instead of saying "he died in his sleep".

My ordinary day : )

Hi, my name is Jeong Hoon Lee from south(South) Korea. This is my first notebook : ) so, from now on i`m about to write just diary of today. (So, i'm going to tell you about my hectic day)

I really didn`t want to wake up early this morning but i ( I)  had to go to work. I got a hangover when i (I) woke up because I got drunken (was drunk) with my seniors and friends at last night. I had taken a shower (my shower)  and got out of my home without having a breakfast. as soon as (As soon as) i got out of my home, i (I)  felt terrible, because it was freezing outside. furthermore (Furthermore, )I have feeling sick during on my way to work. (I felt sick all the way to work). I was eager to have hangover stew. (what is hangover stew?)

Fortunately, I passed away my work time without any trouble ( I managed to finish my work on time without any problems. P/s : "to pass away" means "to die") : ) after an hours (After long and tiring hours) I can go (return) to my home! as soon as i (As soon as I) get home, I will take a shower and have a conversation with my girlfriend on the phone. I hope that the weather of tomorrow will be nice. (tomorrow's weather will be better than today)

Thanks for reading my notebook! Have a nice day everybody : )

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화이팅!