The pain you are experiencing is from holding the breath back with the vocal cords, also called "pushing." Literally, you are pretty much closing the vocal folds, letting little air through and pushing the air against the cords, letting a tiny stream of air through.  Make the tone feel a little bit airy.  Don't try to make your air last forever.  Breath more than you have to.  Breathing is always an opportunity to show/develop one's musicianship by phrasing.  This kind of "pattern" singing often leads to tensions like you have experienced.  My mantra as a singer, teacher, conductor is, "The voice is breath."  In the case of you director, the "spirit" is breath.  I would still agreee that she might not be knowledgeable about vocal production, though her musical and stylistic understanding may be superb.  Try making a tone that is akin to the voice that comes out when you yawn and speak simultaneously.  It's a bit extreme, on the other end of the spectrum from what you are doing in your warm-up, a habit you want to break.

 

Good luck.