How do i pass access denied websites at public libraries

One thing I can think of although there might be other alternative implementations...

All PCs in the library go through web proxy and proxy is the one filtering URLs. Your browser have a setting for proxy server. You need to disable it. Even when you disable it, the library network may have restrictions that only allow PCs to talk to proxy server instead of directly to the router.

Most of the time, Windows in public PCs are severely restricted via registry manipulations that you'll find most functions disabled. The trick is to find something people forgot to disable and re-enable some functions.

if your going to try using a bootable environment id suggest using a standalone dns server like opendns so you dont have to rely on the libraries router.