Theming Views Display
Try this:


on the view edit screen click on the display you want to theme
click on the "Advanced" tab so that it slides down
in the "Others" section click on the "Theme: Information" link
in the "Row style output:" section you'll see the template file names you can use, you are currently using the one that is bold, the last name is the most specific, i.e. something like views-view-fields--VIEWNAME--DISPLAYNAME.tpl.php


simply copy views-view-fields.tpl.php from the "theme" directory of the Views module to the directory of your theme, rename the file and modify as you wish (and clear the cache)