Sitting too much also tightens the hamstrings, which can cause back pain. Tight hamstrings are pretty easy to diagnose: bend at the waist and touch the floor. If you can't touch the floor (even better, put your palms flat on the floor), you need to stretch. Stretch out the hamstrings and hip flexors and see if the pain goes away. You may need to do it every day.
You probably didn't hurt yourself lifting, if you did, you probably would have noticed it when it happened. Sitting all day is just not good for you, that's the most likely explanation.