Diary #5

I made up with a friend today.

(to get along = to be compatible with, to like each other, to make up with = to resolve a problem in a relationship)
I had wanted to or I had been wanting to apologize to him for a long time.

(past perfect here or past perfect continuous because the state of wanting lasted for a long time until it was completed (in the past), when you made up with your friend.
And today, i said I was sorry.

(reported speech is written in the past tense. Using quotations is correct, but it sounds more natural to say "I said I was sorry" than to say "I said: 'I'm sorry"'
We've started to talk again (in general), or We started to talk again (in that moment).
So I'm very happy now.

Good job!

Diary #5

I got along with a friend again today.
I wanted to apologize to him for a long time, and today, I said ''sorry''.
We started talking again!
So I'm very happy now.

[I'm glad to hear that.]