The reason the link isn’t working is because you haven’t formatted it correctly.
This:
return '<h3><a href="www.google.com">Hello World</a></h3>'.$content;
Should be this:
return '<h3><a href="https://www.google.com/">Hello World</a></h3>'.$content;
To answer your other question: There are a lot of social sharing plugins that will add sharing links to your content.