My cousin is sick!

My cousin (I call him '오빠(oppa) in korean) is sick!
A few days ago he said to me, "I'm getting sick, my legs hurt."
At that time, we didn't care about his pain. I just thought it was is normal pain because he had hurt his legs a long time ago. So sometimes he used to say that.
But today, his legs got in big trouble! His legs swelled up!
So we have to go hospital. I'm applying an ice pack to his left ankle.
I'm really worried about him. I really like my cousin,
So I hope he will be fine.

Sounds awkward. We don't say it like that. maybe, "there was something seriously wrong with his legs" would be better I think.

Small corrections.

I hope your cousin is ok. :(

My cousin is sick!

My cousin (I call him 오빠(oppa) in Korean) is sick!
A few days ago he to said me "I'm getting sick, My legs hurt.'
At that time, we didn't care about the pain. I just thought it was normal pain. Because he hurt his legs a long time ago. So, sometimes he would say that.
But today, his legs got into big trouble! His legs swelled up!
So, we have to go to the hospital. I'm applying an ice pack to his left ankle.
I'm really worried about him. I really like my cousin,
So I hope he will be fine.

My cousin is sick!

My cousin (I call him '오빠(oppa) in Korean) is sick!
A few days ago he said to me 'I'm getting sick, My legs hurt.'
At that time, We didn't care about pain. I just thought it is was normal pain. Because He his hurt legs hurt a long time ago. So, Sometimes he used to say that sometimes.
But today, his legs got are in big trouble! His legs swelled up!
So, We have had to go the hospital. I'm applying an ice pack to his left ankle.
I'm really worried about him. I really like my cousin,
So I hope he will be fine.

Underlined: It sounds weird to say it like that. We usually say "there was something really seriously wrong with his legs." That sounds more normal to me.

Green: Capitalization errors. You usually don't capitalize words like his or he when they are in the middle of a sentence, only when they are at the beginning.

Yellow: Words that needed to be added