I would be looking at sharing someone elses horse, and the expenses. I think I am just worried I would not be good enough, or not treat the horse right (as I am used to school horses who can be dead to the leg or really hard to slow down). Also, would I be able to learn things if I shared a horse, and is it worth stopping lessons for?
Don't worry about your learning stopping if you stop taking lessons.
Lessons are wonderful, even indispensable for certain stages of learning, but you will definitely continue to learn if you stop taking regular lessons and start sharing a horse.
As far as "not being good enough" goes, sometimes we are our own harshest critics. You are clearly well aware of the differences between your school horses and non-school horses, and the changes that you would have to make as a rider to accommodate those differences. Based on your posts, I have no doubt that you would treat the horse right.
One of the best ways to improve as a rider is to ride different horses. Lesson barns might let you ride a different horse every week, but you'll usually be missing out on what you can learn from riding a horse who isn't dead to the leg or dull in the mouth.
Probably the most ideal sharing situation for you would be to find an older, more experienced rider with a been-there-done-that horse, who is willing to help you out, answer questions, and offer advice. Even something like a partial lease might be worth looking into - more often than you'd think, children and teens outgrow horses in terms of ability, and would rather partial lease the animal to a younger/less experienced rider to learn on, rather than just sell it.