Though I certainly don't have chest-related back pain, I recovered from a pretty painful athletic injury to my back. One of the most useful pieces of advice I received from a doctor was to learn exactly how each "pain reliever" works.
Some pain relievers simply block our ability to receive pain messages while others actually block prostaglandins, the chemicals which incite inflamation. Aleve is one of these sorts of medications and is apparently chemically similar to the prescription medication Naprosyn, which my ex girlfriend was prescribed for her back pain.
In the end, the solution to my back pain was an odd one- I had to strengthen my stomach muscles. My ex, whose back pain was almost surely related to her chest, followed the same advice and felt so much better that she changed her mind about a reduction.
For what it's worth ;)