public library

[output]

Is the following sentence correct and natural?

I went to public library to borrow the books 2 days ago.

 

[emsr2d2]

Is the following sentence correct and natural?

I went to the public library to borrow the books 2 two days ago.

Note my corrections above. Write the numbers one to twenty (inclusive) in full (words, not digits).

Using "the library" and "the books" work as long as the reader/listener knows which library and which books. Otherwise, you need "I went to a public library to borrow some books two days ago".
There are alternative word orders too:
Two days ago, I went to a/the public library to borrow some/the books.
I went to a/the public library two days ago to borrow some/the books.