It could be Psoriatic Rheumatism!
A wider family member recently had some tests when they had severe back pain and were told that there was a connection between that and their Psoriasis. First time I’d heard of it but sure enough when I looked it up it’s called Psoriatic Arthritis. Other possible symptoms include iritis and spondylitis. Google psoriasis back pain for lots of links! Then go back and see your doctor if he hasn’t already made that connection!