Q. I have a question, may I know is there any public library that I can sign up and read books free online? :)

There are many, most public libraries in the US offer this service, it just depends on your location. All the public libraries in the Galveston/Houston area have eBooks available. Some of these libraries only require that you be a resident of Texas, others require that you be a county resident. 

If you don't live in the Galveston/Houston area, you can google public library to find ones close to you. Normally all that is required is that you be a resident. Many libraries are allowing online registration for library cards. Once you have a card you can borrow eBooks.

There are also free collections of eBooks online that you can try, but they will generally have older content. Open Library is one of the best. You'll just need to create a free account at archive.org.