I just downloaded the 'Font Awesome' (from http://wordpress.org/plugins/font-awesome/) plugin and I have just installed and activated it on a fresh WordPress install on a 2013 theme.
Using the 'Font-Awesome' dropdown inside of new posts, I was not able to get any icons displaying.
But using the provided short codes that come with that plugin I was able to get the icons to display properly.
If you use the above method to include 'Font-Awesome' icons, and then use my plugin to include more icons you will have no issue.
I was able to have both plugins active and displaying icons properly as intended, using the following code:
[icon name=icon-pencil]<span data-icon=""></span>
The first icon is a font-awesome icon. The second is an icon from my plugin.
Ultimately the problem lies in the 'Font-Awesome' plugin and the way you are choosing to display their icons. Hopefully I was able to help you out and resolve your issue.