I have been doing yoga since I was 12 years old. Miyagi said in that movie (Karate Kid) "there are no bad students, only bad teachers."
I have read articles in yoga magazines that people that did not have a perfect neck have caused serious problems from the
plough pose. Maybe you did something harmful while doing it.
Bikram's yoga does not have it. Also Bikram yoga people would say it is too cold. They keep their room at over 100 degrees. They feel that this is important. But you are doing OK for a room too cold. Also their order of postures loosen you up more and more.
Try different positions that stretch those muscles. You can always see a doctor to make sure that you do not have a medical problem like lockjaw. "Tetanus often begins with mild spasms in the jaw muscles (lockjaw). The spasms can also affect the chest, neck, back, and abdominal muscles. Back muscle spasms often cause arching, called opisthotonos."
It is up to you to figure out if it is a serious problem or you just need more patience. If you do a search for danger of plough position maybe you can find something, but this magazine had an article about it with bad stories from yogis. Here is a book on yoga from a medical doctor for under $15.
Amazon.com: Yoga as Medicine: The Yogic Prescription for Health and Healing Timothy McCall