Not being able to take a deep breath without pain is different from dyspnea. It is called costochondritis. It tends to worsen when taking a deep breath, coughing, sneezing or with any chest wall movement.
https://www.mayoclinic.org/diseases-conditions/costochondritis/symptoms-causes/syc-20371175
This condition makes you think you are short of breath because it hurts to breathe. When you don't take a deep breath that causes anxiety. Shallow breathing also causes atelectasis of the lungs when tiny air sacs within the lung, called alveoli, lose air. When this happens you will develop a dry cough except coughing makes your rib cage hurt.
https://www.mayoclinic.org/diseases-conditions/atelectasis/symptoms-causes/syc-20369684
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Is costochondritis (rib cage pain) the problem? I had it several times. My rheumatologist said it is common with inflammatory diseases and there wasn't much she could do about it. She said it should improve on its own and it did.
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You might want to get something called a pulse oximeter. That will tell you if your oxygen level is low.
https://www.lung.org/lung-health-diseases/lung-procedures-and-tests/pulse-oximetry