Dogs exhibit back pain by decreased jumping, less to no feeding, roached back (rounded up),and sometimes paw licking. Paw licking may occur since the nerves of the back go to all 4 paws and if there is a pinched nerve your dog may lick the involved paw to help the neuralgia ( numbness ).
Having subluxation ( bones of the spine that are stuck and irritating nerves ) will commonly cause back pain. A subluxation will occur from age, jumping, athletics such as agility, arthritis, cruciate ligament injury, and of course disc problems. There are many more causes but these are the common ones.
What should you do? First make sure your vet has cleared your dog of any diseases. Call an animal chiropractor to have your dog adjusted to correct the subluxations. I have been in practice for 30 years and I teach at Options for Animal Chiropractic College and I can tell you that most vets are not educated in spinal biomechanics or subluxation diagnosis, so they will typically not recommend a chiropractor.
You can find a board certified chiropractor on the American Vet Chiropractic Assoc web site. I am accepting new patients so please call me at 781-337-1180 or email Dr Bruce at firstname.lastname@example.org. All my visits are at your home which adds an element of comfort for your dog.