First of all, never lunge a horse in just a halter. Use a loose ring snaffle and run the lunge line from your hand, through the snaffle ring, up over the back of her head behind the ears and then back down clipping it to the snaffle ring on the opposite side. Put a saddle on her and side reins so she has light contact in a relaxed, standing position. NOW lunge her. Every time you have to change direction you will have to stop and change the rig (this is why a lunging cavesson is good). Doing this you will have much more control.
When you lunge the rein hand the the whip hand form a triangle with the horse being the base of the triangle and the handler at the appex. Point the whip at the horse's hip. If she refuses to move step rearward and point the whip at her butt behind the hip.. and crack it. You may have to reach out and touch her with it.
If she gets going too fast you point the whip toward the girth of the shoulder.
Lunging is an art form. Lunging a horse in a halter teaches nothing and the halter is mild so if they decide to take off, they are gone.. you cannot stop them. Never wrap the lunge line around a hand or any other part of your body.
Reading what you have written my impression is that your lack experience. I suggest you find a place to keep this mare where she can be trained and you can take lessons. While any horse handler can be stepped on, this problem is most often the result of an inexperienced handler not knowing how to move to NOT be stepped on. I am not saying this to be mean.. it is just that green horses and green handlers usually turn to black and blue.
Never forget.. horses are large and not terribly bright (sorry Walt Disney). They can kill you and without intention. Do stay safe.