Not necessarily, although your risk for back pain is somewhat higher. Having swayback posture means that your back is arched and your upper back is rounded more than usual. Extra weight on the abdomen–which you will definitely have in the next nine months–also tends to make the lower back arch more. Too much arch can be a source of back pain.
You may be able to prevent problems by using good posture. Stretching and strengthening exercises may help. Good flexibility is especially important in the front thigh muscles, and strengthening your abdominal and back muscles can help support your spine. Talk to your doctor. She or he may recommend that you work with a physical or occupational therapist to develop an exercise program for your pregnancy.