Solution:
Before using $j
you should declare it using .noConflict()
.
You can also use it for your plugin, WordPress require it most of the time because it use different libraries.
So at the to of your plugin write:
var $j = jQuery.noConflict(); //$j could be also j, or $r, everything you want, is a variable.
Then replace all your $
with your new variable used in the no conflict.
Hope it help.