Your teacher is negligent! You needed instruction in how to halter & lead & control a horse & the more advanced groundwork first!
Surely that's clear to you at this point, yet still unclear to your teacher, because he/she endangered your welfare & the horse's welfare by not starting at the beginning with you, & then when she had to rescue you & horse from whatever WOULD have happened, she STILL didn't get herself on track & revise her "teaching" program for you & horse!
You must discuss what's happened with your parents, they must understand that this "instructor" has been negligent, & then it's their call to decide whether to discuss with "instructor" or find you another teacher who'll keep you & horses safe.
"Instructor" also has given you no help with handling fear, it seems no horse psychology/info on "reading" the horse's intentions/thoughts/moods before the horse takes a particular course of action. For example, you should've been taught to see the mare's idea well in advance of her taking over leadership to the point that she left, so that you could've maintained control of her.
Both you & mare are fortunate that you weren't hurt or worse.