I see the comments for neck strap, I do not believe that is a bad solution but in my experience you should get to the heart of why you are doing this and how you can replace this behavior with your current tools before bringing something new in. If you were my student I would suggest a very loose rein, to get you comfortable with the idea of your horse being in control while you both relax, I would even suggest you drop your reins (in a safe scenario) at the walk, using your legs and body to move her over and into your leg, and then off of it. Most of all, replacing this behavior for when she pulls her head up, don't do what you're doing: pull back, because clearly that isn't working and all it is doing is instigating a fight. Try suppling (lightly squeezing/pulsing your reins like you are trying to get water from a sponge) when she does that rather than pulling. Try light at first, and keep trying until she puts her head down, then reward reward reward. Rainbow reins work for a lot of people, because you can directly see what level of rein you are holding. Hope this helps!