Have you noticed if it ever goes away entirely? I get that on and off and have thought it was intercostal pain as I have COPD and sometimes breathe pretty hard.
Do you have arthritis? I'm wondering a bit now if it could also be arthritis irritating the nerve root as it comes from the spinal cord. I currently have shingles

, and before I noticed the rash I woke up in the middle of the night a couple of times wondering if I'd done something to crack a rib, they ached and I had a couple of sore spots. I'm really not sure if it related however. You should probably get it checked to rule out anything serious.
Judi