GreyFriar, I have no idea what the Heraldry website is or how it’s supposed to work, but I tried searching for my old unit, 366th Tactical Fighter Wing, and it came up with nothing.
Here is a link to the TOIH Air Force page:
http://www.tioh.hqda.pentagon.mil/Catalog/Category.aspx?grp=1&menu=Uniformed%20Services
I didn’t find you old unit either. You might try the USAF Historical Research Agency website: http://www.afhra.af.mil/