I like your mare a lot, and yes she is green indeed! She has no mouth yet and this is not the way to put put one on. She is having a very negative reaction to pressure on the bars. This is caused by 2 things: 1) Your hands low and wide and 2) The running martingale. Right now, she needs to learn to carry herself in a neutral position. This means no hand interference from the rider or confusion/punishment of hitting the running martingale.
Firstly, I don't want you to get a broken nose either, so get a standing martingale pronto. It will stop the horse from flinging it's head up without messing with it's mouth.
Secondly, I know your trainer told you to ride like that, but it's wrong for this horse right now. Put your hands together and either ride on a loose rein and touch it when you need to give direction to the horse or ride in a light contact, straight line from elbow to bit and follow the horse's mouth with a soft hand. The later will hold the bit more into the corners of the mouth and less on the bars. When she flips her head around you do not resist, you simply follow with your hands and continue riding forward. If you try to pull this horse into a frame now, it will continue to resist and learn to fear contact and the bit. In my experience with Arabs they will turn into curlers to avoid contact.
Aside from the mouth issues, you need to take a more assertive role when riding this horse. You tell it where to go and how fast to get there. And for the love of Pete don't let the thing rubs it's head on it's leg while you are on it. That's both disrespectful to you, the rider and dangerous. If you would like to me expound on that last point, just let me know and I'll tell you why. Lastly, your attire is not appropriate for riding and especially not for riding greenies. I say this purely because I am concerned for your safety.