Definitely go get it checked out.
I was turned down on my first application to join up due to bad knees, I had to wait 6 months without any pain before I could re apply. Now I'm glad I got it sorted before joining, going to basic trg with an injury would be a very bad idea
Having a bad back is not something that you will be able to 'hide' in the Army. I have a occasional recurring back problem after an accident in Iraq in '03 and when it's bad, I can barely move let alone attempt to 'hide' it.
Can you trace the bad back to any injury, heavy lifting etc? Where does it hurt? How old are you? Do you have a temperature or any signs of infection? Is there a family history of osteoporosis or ankylosing spondilitis?
See how useless an internet diagnosis is? If you have a bad back, they're probably right to defer you! How is running up and down with a bergen going to aid recovery??
Don't be silly, go to your GP, get a proper diagnosis and THEN worry about what the army will say!