Just wanted to share my experience with a similar problem. I recently ended up with a pretty bad case of breathing issues that sound a lot like what many are describing. Inability to take a full, satisfying breath which leads to obsessive need to get a full breath - causing constant (every minute, all day long) sighing and yawning. I would be pace around the room in the evening in complete desperation to take these breaths and it was a very debilitating experience. I noticed that it seemed to happen shortly after a particularly nasty business meeting. Never woke up at night and also seems to go away when in a sleepy state (laying in bed awake in the early morning or late night). As soon as I was fully conscious - it started and lasted all day. I would wake up and as soon as I remember about the breathing issue, I would attempt to keep breathing normal and calm as I would be breathing naturally - and this would work until my mind would take over and start to go into the vicious cycle of trying to "take that deep breath". Would not get worse or better with activity. This went on for several weeks. Nothing could distract me from it or take my attention away.
From researching online and from the patterns, I was pretty sure that there was no issue related to lungs or heart. Based on when it seemed to have started, I was pretty sure it was stress related. Decided to avoid going to the doctor as I felt the tests attempting to find a likely non existing issue would just add to the problem and likely help develop a deeper habit that would be even harder to break.
What helped me: I started to work on assuring myself that the problem is phycological and I would not actually suffocate. I would try to "extend" those moments when just waking up (when the problem was not noticeable) by continuing slow and controlled breathing as I was laying awake in bed and use that as "proof" that there is no issue. Problem would still persist as soon as I would get up and stop the breathing 'exercises' but it was important to assure myself of the nature of the problem. Attempted to take some Bendadryl to increase sleepiness in the evening and relax. If it did make me sleepy (which in most cases it did not) - it helped. Little by little, the problem would start to get better. Not much and not for long, but it would give enough reassurance. Used those moments to further "teach myself" that this is just a cycle that needs to be broken. I very much believe that "some reassurance" helped a little, which would improve the issue briefly or a little and then I would pay very close attention to these patterns and use those positive moments to further reassure myself and it would build up and build up and improve. Negative thoughts on the other hand (feeling of desperation often times) would make the issue a lot worse. Ended up going to a wedding and realized that the issue did not come up at all as long as I did not remember about it at the wedding. Still came up a bit in the eve but I was now 100% sure and this reassurance helped remove the problem completely within the next few days. The key I believe was that I was already in a "positive and assured state" that the problem is resolvable by the time of the wedding. I believed it 100% due to the things described above. Until that day or so, nothing could have distracted me from the breathing issues.
I wanted to share this in case anyone is experiencing something similar. Obviously causes of the same issues can be varied so please do not skip out on medical attention if you feel you need it.
Interestingly enough also, I spoke about this problem to a couple of people and two of them mentioned that they started to experience the same thing several days later. As if its something that creeps into your mind and causes a problem.
I suspect also that the initial trigger may have been stress itself as I mentioned OR just simply really fast and over-stimulated speaking at the business meeting that ended up in a conflict. Then perhaps I needed to catch a breath but continued to speak in such a way and it caused something that I later noticed and once I noticed it - the pattern began. I imagine that the same thing can happen with exercise?
Its difficult to describe it, it is so strange.