A compression fracture can take about three months to heal. Bones will continue to remodel for up to 18 months. This means you are only about halfway through the first steps of healing. There is no reason to believe you'll always have pain, though people who've had a fracture like this often end up with some ongoing, low-grade pain. This is especially true when doing heavier activities.
Be patient, and follow the advice of your doctor. You should notice more pain relief once you've started your rehabilitation program, which usually begins about six weeks after the injury.