Blue means it's good to use it.

Red means spelling mistake or sentence structure.

Bold means correction

-> means a new sentence.

------------------------------------------------------

exam ~~~~~~~~

ㅣI am a student in Univ.
i majored in tuorism tourism management. (Like EssexYaYa said, it should be "tourism")
i have a term exams. (Like EssexYaYa said, it should be "midterm"/"final examination")

start to monday ~ finish to sunday.

-> It starts from monday ~ and finishes on sunday.
so I am really tierd tired today ~ 

i remain 5 subject exams.

-> (Like EssexYaYa said, it should be "Only 5 subject exams left/remain".)
korea Korean education is too competitive ...
but i don't never give up(I think "but I will never give up" is a better choice)

죄송합니다..난 미국 네이티브는 아니야 ㅠ.ㅠ

Your English was pretty 긋. Good luck with your exams. 화이팅~

exam ~~~~~~~~

I am a student in Univ.
I major (1) in tourism management.

I have a term exams (?). I have midterm exams.  

I start on monday ~ then finish on sunday.
So I am really tired today ~
Only 5 subject exams remain.
Korean education is too competitive...
but I don't never give up

Bold=Correction
Italics=Alternitive
(?)=Not sure if (that) is what you meant

Notes: 

(1) (If you are still studying Tourism Mangement you use present tense, but I'm sure you already knew that ㅋㅋㅋ)

Good job, keep up the good work! I also hope you do well on your exams!