With any premium account, just select the "public tracking" option for your link and share the tracking page with your client. If a link is never used on the internet or shared publicly then it doesn't exist in a cyber sense. Finally, Event Tracking employs an object-oriented model that you can use to collect and classify different types of interaction with your web page objects. Our favorite is YOURLS, but Lessn More is another good free option.
See if you are using Classic Analytics (ga.js) or Universal Analytics (analytics.js).