If your thumb is hurting, it is because you are lifting the weight of the saxophone with your thumb. The weight should go almost entirely onto the neckstrap. The thumb is used only to steady the saxophone. You should adjust your strap so that the mouthpiece fits exactly into your mouth without lifting at all with your thumb.
It might be that lifting the sax with your arm for an hour is what causes your back to hurt. When you adjust the neckstrap correctly, perhaps your back trouble will be eased. If not, you might consider the sax spinstrap, a shoulder sling that distributes the weight away from the neck. See
http://www.wittman-spins.com/spins.html for a discription.