I'm so tired.　good 

My school started today. good
I had English and science. good
So clean in school. (the school is so clean [?])

It's very cold. good
The cold gave me goosebumps. good
But can turn my all homework to my teacher. (but of course I turned in all my homework to my teacher [?])

Of course.

I was on day duty today. good
I say "yoroshikuonegaishimasu".Just then everyone of in my class follows to me (and repeats by saying) "yoroshikuonegaishimasu"
I'm so tired... good
I will get enough sleep. [日本語でなんと言いたい？]

I think it's good! :D

I'm so tired.

I started school started today. (School began today.)  
I had English and science.
It's so clean in school.It's also very cold.
The cold gave me goosebumps.
But of course I could still turn my in all of my homework to my teacher. 

I was on day duty today.
I say "yoroshikuonegaishimasu". Then everyone in my class says "yoroshikuonegaishimasu" back.  
I'm so tired...

I will get enough(lots of) sleep (tonight).

Hope this helps!