Pain left rib cage goes around to the mid back?

Could be rib problem: I see this problem very commonly in my osteopathic manipulative medicine practice. Ribs normally move up & down with respiration & are quite flexible. Sometimes, the rib gets 'stuck' losing both its ability to move & its flexibility. Some serious health problems can cause this, but usually it is just a tight muscle or ligament & can be easily fixed with osteopathic manipulation.

Chest pain: Chest pain always should be investigated. You may have muscle spasms, costochondritis, acid reflux or something sinister like a heart attack, aneurysm, rupture esophagus etc.