Norton Security is very good software, for many people you can install and forget about it and it'll take care of your PC.
As to your issue with browsing, have you tried to repair Norton, what did you have installed before, what browser extensions, or any other security software installed?
In some cases left over files from previous software can cause many issues.
If you haven't already I recommend posting your
Security Configuration Wizard, include details about your OS, Security, and Browser Extensions.