最近我很忙。

生病了! 我觉得虚弱得快了恶心死了！星期我五我感觉好些了比较好，我有上了一节汉语课. 我们学习了联系中国才菜。很有意思的课！
周末太热不想去外面，所以我跟我的朋友们一起玩了视频游戏。

最近我很忙。

最近我很忙。

when you mention about time, don't forget time is a modifier. and in Chinese, we always put the modifier in the front.

所以 always follows a comma.

病 is also a verb.

so you could say:

我病了。

我病得很重。

我病得快死了。

最近我很忙。

上星期太忙了！星期一早上我气息行（起床）7点半，我去看医生9点。②（我在星期一早上七点半就起床了，然后在九点的时候我去看了医生）

医生很忙所以我等（了）45分钟！在我看过医生的时候她给我抗生素。③（医生帮我诊断并让我服用抗生素）

中午我去了大学。我在大学（里）帮助我的朋友。

我们的大学有电视工作室。我主持一个电视节目！

星期二，星期三，星期四药物让我生病了! 我觉得了（自己都快）恶心死了！

星期我（五）我（感觉）比较好，我有一节汉语课，我们联系（练习）中国才（菜）。（这是一门）很有意思课！

周末太热去外④（周末太热了以至于我们不能外出，）所以我跟我的朋友们一起玩视频游戏。

修改建议：

①“生病”在汉语里是一个动词而非形容词，“我很生病”在语法上是不通顺的，所以换成“我也生病了”会更加妥当；

②在汉语中，状语的位置比较灵活，但此处的“at 7.30 on monday moring”作为时间状语一般放在句首或者句中比较恰当；

③此处可以灵活处理，对原文意译一下，同时，在汉语里表示“看病”时，一般是“医生给我看病”，而不是“我看医生”；

④“too...to..”结构可以翻译成“太...而不能...”。

以上，希望能帮助到您~

最近我很忙。

You did good job. Just keep trying：）

Recently I was very busy, I was also very sick. last week was too busy! I woke up at 7.30 on monday morning, at 9am I went to the doctor. The doctor was very busy so I waited for 45 minutes. When i saw the doctor she gave me some antibiotics. At noon I went to uiniversity. At university I helped my friends. Our university has a Tv studio. I hosted a TV show! Tuesday, wednesday, thursday the medication made me sick, I felt so sick I could die! On friday I felt better and had a Chinese lesson. We studied Chinese food. It was a very interesting lesson.
The weekend was too hot to go outside so I played video games with friends.