I recommend you download Microsoft Security Essentials (it's free and works) http://windows.microsoft.com/en-US/windows/products/security-essentials
Go to Control Panel > Appearance and Personalization > Folder Options
In there is an option to "Show hidden files, folders and drives" check the box next to this. You will now be able to navigate to and see the files.
To hide the files again just do the same thing but un-check the box.
The AppData folder is mainly temporary data so you can delete most of it without any consequences. C:\users\shawn\appdata\
* * EDIT: Most internet browsers store up to 800 MB of files, if it is less than this amount then you shouldn't worry about it.
* * EDIT: This does sound like a messy problem. What you should do is try to figure out which program is writing all these files to the folders. When you notice the files are being written, open up "Task Manager" and see if there are any unusual processes using a lot of ram or cpu. Look up the process on Google to see if people are saying if it is a known virus. Once you are sure it is a virus, you can then disable it or delete it.
Also, open up "System Configuration" by typing msconfig.exe into the start bar. Go to the "startup" tab and uncheck anything that you are not sure what it is (Do NOT uncheck anything from Microsoft and don't change anything in the other tabs).
Good Luck and i hope you can figure out how to remove the virus. You can try Malwarebyte's Anti-Malware free version. That program can get rid of some pretty bad viruses and you can just remove it after your'e done (http://download.cnet.com/Malwarebytes-Anti-Malware/3001-8022_4-10804572.html?spi=7699aba41e96695872cc90cd3debd097 ).
If all else fails you should re-install Windows (make sure you backup your important data).