The First Rule of Riding: Keep the horse between you and the ground at all times!
I'd have three recommendations: (1) Make sure you trust your instructor. That person is the best source for improving your riding because she'll be doing so in real time. (2) As there is always more to learn, enjoy the process of learning like a mountain climber enjoys the process of ascend (rather than merely standing on the summit). (3) Try to remember to treat your horse as a partner, not as exercise equipment, even if it's "just" a lesson horse. It likes praise and attention just as much as a Million-dollar race horse, and it hates stress and hassle just as much as you may.