Is it important to have an anti-virus application running on your phone or does the carrier protect it? I use my phone like I do the computer.  Shopping online with a credit card etc.  Surfing unknown sites... Does my phone require an anti-virus application to protect the internal drive of my phone? Can it be damaged by a virus like on a computer?

OS: Android 4.1.1
Phone: Samsung Galaxy S3
Android is an OS built using Linux, which is fairly resistant to viruses. Hence primarily there is no need to have an antivirus software in your mobile device. 

As in your case, if you are browsing unknown sites, there is a chance that you will be attacked my malware and adware (which are very truoblesome programs and which cannot harm your moblie, but show ads, popups, etc.)

Also these malwares tend to come from the apps installed from unknown sources. Always install apps from the Play Store itself and you will be safe from the majority of malwares.

As a precaution, do not use untrusted sites and never enter your financial details into sites that do not have secured connections (https). 

If you have to install apps from unknown sources, it is better to have a antivirus software, just to be safe. But keep in mind that any of those software cannot do much in protecting you with the transactions entered into with unsecured sites other that showing a warning.

Oher than that, the need for an antivirus software is very remote.