It is difficult to know the origin of your back pain without taking further history from you followed by a physical examination.
Your GP may have already done this with you. For example asking questions about how this pain has come about, was there anything that triggered it, is there anything that makes it better or worse. What is your previous medical history?
A physical examination should take you through your range of motion; ie how far you can move in all directions compared to how you moved before, the orthopaedic part of the examination should help eliminate any underlying mechanical problems and a neurological examination to help determine if there are any problems with the messages from your brain being relayed to the parts of your body. Specific muscle tests can also help determine if the muscles of your back are involved.
The history and examination help to determine where the pain is coming from. It helps the practitioner determine if it is the structure of your back (eg the spinal /vertebral joints), the nerves (the messages) and or the muscles which are the prime factors in your back pain.
Exercises may help your back and in the long term help to strengthen it. However if the underlying cause is not corrected then exercises may not help.
As you have had the pain for a month seeing a chiropractor may help you to get to the cause of the problem. You could try to see if there was a chiropractor in your area that offers a free advisory consultation. This may provide you with some more information about your back pain and you would be able to see if chiropractic was suitable for you.
Interestingly, NICE recommends chiropractic on the NHS (especially if it is chronic in nature, lasting for more than six weeks). Read more here http://hubpages.com/hub/Chiropractic-on-the-NHS. You could ask your GP about this to see if your practice can offer you chiropractic on the NHS