If a rib is out of place, it can disrupt the surrounding musculature as well. It will put the length/tension ratio out of whack by altering the attachment points of those muscles attached to the ribs. It may also effect your T-Spine mobility as well as effect proper scapular motion. Also, your body can sense when something isn't "quite right" and will react accordingly.
If your body senses the rib out of place, it will cause the surrounding musculature to spasm in order to guard and protect the area. Just like with an ankle sprain - you injured the ligaments in your ankle, your body realizes that, and reacts by causing the surrounding muscles of the ankle to spasm and guard in order to restrict the movement at the injured area.
Now, I'm not saying that you definitely have a rib out of place - just saying that it is a possibility based on the symptoms you listed initially. The T-Spine mobility and scapular motion/stability may be the major cause as well. It could also be stemming from thoracolumbar fascia tightness, latissimus dorsi tightness, paraspinal/errector spinae tightness, etc. The body works as a unit and if one link in the chain fails, another link needs to make up for it.
You are probably correct in that the symptoms are coming directly from a muscular issue - so you can get the ART/soft tissue work, ice/heat, etc to relieve the muscular symptoms and improve the muscle tissue quality.
But the BIG question is - What is causing the muscle to have the symptoms/become injured in the first place? Weakness? Imbalances? Structural issues? You have to find the root problem. If you have a leak in your roof, you don't just put a pot under it to collect the water - you fix the leak.