You are definitely on the right track by walking and doing yoga. Certainly, you are not alone in dealing with this back pain either: according to the American Medical Association, four out of five adults have suffered from chronic back pain. In the past people were told to lie down and rest to deal with their back pain. But more recently we have found that such advice actually contributes to more pain and disability due to the weakening of muscles. Now doctors are advising patients to get (or stay) active as a way of dealing with back pain.
Walking should not exacerbate a back problem, and is it important for overall health. Be sure to replace your exercise shoes often, as the support your shoes lend is critical. Yoga and other exercises designed to improve your flexibility have been shown to reduce risk of back injury, so this is excellent for you to continue. In addition, you should definitely add strength training to your routine, especially exercises that target the abdominal and the back muscles. Strengthening these muscle groups will likely help to alleviate some of your pain, as weak back and abdominal muscles are often contributors to chronic back problems.