With my head forward, I look like a turtle. Working with small children is guaranteed to strain your back.
Good posture has a lot to do with balanced muscle strength.
Pay more attention to the way you sit, stand and stretch. And strengthening the upper back muscles, as you mention, might help. The muscles you need to work are the rhomboid and lower trapezius muscles, which pull your shoulder blades together in back. Sit upright in a chair and simply pull your shoulder blades together. Imagine you are trying to squeeze a tennis ball between your shoulder blades.