While there is pain associated with COPD, whether it's muscular, cramping, chest tightness or skin tears, these are all what I think of as "related pain" or "auxiliary pain", as opposed to pain caused directly by COPD. If your appendix is infected, it causes direct pain. With COPD, everything you mentioned is a result of something else that happens because of the COPD: coughing, cramping, hitting yourself and causing a bruise or tearing of the skin. Pain because of rubbing of the lungs against the pleural cavity walls is another sort of pain. I guess my point is that while all these painful things are associated with COPD, it's important to recognize that the lungs themselves have no nerve ends and can't cause pain in and of themselves.
People need to understand that so they can determine what kind of pain it is to describe to a doc. If you say, "My lungs hurt" that isn't descriptive, but if you say "I've been coughing for days and the muscles around my rib cage are screaming" that's very descriptive. When I had a pleural effusion the discomfort was so general and could have been a bunch of other things, including my gall bladder. It took a couple of weeks to determine what was going on. After I had the fluid removed, the pain of my lungs rubbing against the pleural wall was very distinctive.
I guess the point is that you really have to pay attention to pain, since how it's treated depends on what sort of pain it is.