I can understand your reason for wanting to discontinue Norton, but more than likely by clicking that link with any AV brand running may have still infected your system. Threats change daily, or even hourly. The best thing you can do is educate all your computer users in the family to be weary of clicking links in emails, even from friends.
For example, last week I had two friends whose yahoo mail accounts were compromised. I received emails from them with just a few words like "you have to check this out", and a link to strange domain name. I suspected something was wrong right away, and It turned the links did lead to a malicious domain hosting a Trojan. They had no idea their emails were being used for spam until I informed them of the situation. Most people just assume if an email is from a friend or trusted source, then it is deemed safe. That is no longer true these days.
To protect you and your family, you can use tools Like Norton Safe Web, for checking if a URL is safe or a threat.
As another layer of defense use the Norton DNS to block known malicious domains.
You should also look at this "Security Best Practice" guide. It talks about keeping your browser up to date, blocking Peer-to-Peer programs and more.
http://www.symantec.com/business/theme.jsp?themeid=stopping_malware&inid=us_sr_carousel_panel7_best_practices
I hope this information is helpful. You can always PM me if you have more questions.
Good luck,
Thomas