I agree with those blaming your muscles. Getting rack / pannier will definitely help you, but so will strengthening your back. I personally prefer messenger bag to a backpack, but if you have a back pain with backpack, you will surely have one with a messenger bag, IMHO.
Bike fit may be to blame (too long reach) - try riding your bike without anything on your back. No pain = no problem with fit, pain = fit might be a reason for your pain (but then again, it might not be the only one).
HTH