You are describing an issue I have been having EXACTLY. Yours is the only post about SOB the describes the deep breath getting "stuck" so preventing you from getting a satisfying full breath. Also, the fact that it comes and goes and is not associated with anxiety, it just happens randomly. And (although sometimes is worse than others) it is not unbearable SOB, I am able to live with it.
The weird thing is, all my tests are also normal except for a continuously slightly elevated bilirubin.
I am actually an ICU nurse so I have some knowledge about these things, and if a patient asked me about a correlation between SOB and bilirubin, I would also probably brush it off as anxiety. But since I know my symptoms are not anxiety related, I don't know what to think. It is not a normal clinical picture.
My theory right now is actually that the SOB is musculoskeletal in origin. I also have some minor upper back and rib slipping issues – and since your ribs play a crucial role in lung expansion, I thought maybe it has something to do with it. I find the most relief from the deep breaths getting "stuck" when I put athletic tape on my sides and physically pull on the tape outwards (while also leaning forward) to help my lungs expand. It's the only thing I can do to help if I want to take a deep breath.
Another (lesser, but still possible) theory is subconscious panic issues. It is possible to have physiological panic attacks even when you do not actually think you "feel" anxious. It has more to do with some kind of issue in your amygdala – making it a neuro issue. This would involve extensive neurological testing that still might not even result in a conclusive answer. (I have heard of people having this issue correlated with spontaneous anger issues as well – since the amygdala sort of controls emotions).
I have no answer at this point. But I was struck by our similar symptoms and the elevated bilirubin. The bilirubin is not something I have thought too much about.
Have you ever had any back/rib/sternal pain? Or anger problems?