Spot on. A tight set of muscles in the lower back pulls on those around them. Even muscles in the chest can be affected too. Standing for long periods can cause the muscles in the lower back to become stiff. Here are some exercises to try:
1. On your hands and knees, arch up your back, aiming to rock slightly back and forwards. This helps stretch the upper and lower back after periods of inactivity (maybe do it when you get in from work?).
2. Lying on your back with your legs bend and feet on the floor, raise one bent leg so the knee approaches your hands, which then grab behind the knees and pull towards your torso. Repeat on the other side and then try with both legs.
3. Finally, the best thing I ever did was sit-ups. Always start with bent legs and tuck your toes under the edge of a chair to provide a brace and lift the shoulders only (it will isolate your abdominal muscles more). When you get good, lift both your shoulders and straightened legs off the floor, balancing on your bottom. Hands on your ears. Then pull both the legs in and torso up to meet the knees with the elbows. Don't pull the head with your hands as you might strain your neck.
Diet-wise, keep tea and coffee to a maximum of 3 cups in total per day and do consider a liquid magnesium supplement (a company called Salus Haus make one). Together with more stews and casseroles at this time of year, they should up your magnesium levels and help relax your tense back. If those foods don't make you salivate much, try our Atrogel® externally and Atrosan® internally. Both are licensed for muscular pain and are free of any interactions with medicines you might be taking.