What do you mean she holds her head down?
It sounds like she is easily distracted/loses focus.
With this type of horse, you need to be thoroughly prepared and have back up plans incase something goes wrong.
Yesterday the mare I was riding encountered a cow on the way home, where there wasn't one before. She also encountered a work crane and a truck full of loud workmen.
Now she was ready to lose her marbles, but instead I made her leg yield, circle, shoulder fore, zig zag.. flex.. anything to get her mind off of all of that and only focus on riding forward.
And it worked :) Her balking was fine, she didn't spook.
Since this is your 3rd experience with a lesson horse... maybe they should pick one that is less spooky/without-confidence.
I don't think at your level this horse is a match yet. I think in a few more lessons you'll be able to ride her a lot more effectively once you spend some time with a confident horse :)