The problem in translating this sentence is that you only apply "dite" to "inflammatoire". So, we have to find a way to say it is a lower back pain, and then add further details to explain it is inflammatory.
How about "What components in the health history make you think it is a lower back pain, and an inflammatory one?"
I think your original suggestion is good, although possibly a little involved. Certainly, I think in this type of case "dite" doesn't necessarily need to be rendered in English. What about putting the "inflammatory" in inverted commas, thus separating it from the rest of the term? Or possibly what is known as "inflammatory" lower back pain?
Do exert caution with "so-called", though: in English it has a connotation of "well, it may be called that, but that's not really what it is" which is absent in the French.