While it's true that, like any surgery, spine surgery can lead to other problems, paraplegia--or paralysis of the body's lower half--usually isn't one of them. Complications such as infection are far more common.
If the fracture has caused an injury to the nearby nerves, you could end up having muscle weakness or numbness whether you have surgery or not. And if the fracture is putting the nerves at even more risk, surgery may be the best option.
Still, if you're reluctant to have surgery, you should know that you have options. Research has shown that patients who have screws surgically implanted in their spines for a fracture like yours recover more quickly than those who do not, but this difference goes away after a year. Two years after injury, patients who do or don't have surgery feel about the same.
Talk with your doctor about your alternatives. While spine surgery probably won't lead to paralysis, it is serious business. It's important to make the best decision for your needs and condition.