Dear Diarly

Lots of good things happened with me on my to me today.

I fellt better than (I did) yesterday.

I was very sick yesterday, but I don't have alreadny problems anymore.

"But" will help connect the two parts of the sentence smoothly.

I leardnstudied mathe, chemistry and eEnglish today.

(1) "Study" is more appropriate than "learn" here.
(2) The names of languages like "English" are proper nouns and hence capitalised.

I improved my eEnglish vocabulary.

I will regularly revise eEnglisch words every day howso I don't forget ithem.

"English words" is plural, so it should be "them" and not "it".

I would like tello tallesk about my school.

I assume you meant to say "tell tales about my school". Reading on, you don't seem to be telling any stories, so I think "talk about my school" would be more appropriate.

My teacher is very kind and they helped me in themy studyies.

(1) For general facts such as this one, we will use the present tense ("help") The past tense ("helped") would refer to a specific incident in the past.
(2) Note that you're only referring to one teacher here. For more than one teacher, you would say "My teachers are very kind".

But I (also) have some teacher,s whom I don't like.,

You may consider adding "also" so that the writing flows more smoothly from the previous sentence to this one.

Ssuch as my mathe teacher.

I would suggest merging this sentence with the previous one. I have edited both of them to allow for this.

YouThey don't explain things clearly.

I assume you're talking about your msth teacher here. You also need to clarify what it is that they don't explain clearly.

I like chemistry, mathe and biology.

I want to continue learning withstudying thesem.

I would like to be a doctor to be.

My English skills are very lowpoor.

For skills, "poor" would be the more appropriate word.

:(( I hoppe that after lots of exercise,practice, everything will go well.

You need to state what it is you hope will "go well."