Few years ago, I used to read a lot of books.

What you said was right, but "used to" emphasizes you don't do that anymore

Because of that my “reading speed” become fast (has) increased.

"has increased" would be great to indicate you can still see the consequences of that increase today.

I even cacan even read a 200 pages book within a day.

SI start reading fromin the morning and finish it atn the evening.

"I read from morning to night" would be an even shorter way to say it

Siting in a library for the whole day.I used to spend whole days at the library

(Nso nerdy! )

I was so proud aboutof that.

The most used preposition after proud is "of" and this is the only reason why I modified your sentence, which was perfectly right from a purely grammatical point of view

I throught I knoew all the dirty tricks…...

FNow, a few years later, I am reading those books again in at “slow” speed.

I found out I missed so many important points.

I think “I know”ought I knew, but actually, I doidn’t!

As you don't think you know anymore (since you became aware of that problem), I'd use past tenses here

Now, I am so ashame aboutd of my “big mouth”.ego/I'm so ashamed I got too big for my boots

"big mouth" is rather used for someone who talks to much (it works if it was your case), but since you rather seem to be referring to your pride, "of my ego" would fit better here
To get too big for one's boots = behaving arrogantly, often for the wrong reasons