It is best to do everything in reverse order. Relax, and only then take a deep breath. Personally, the video of Schultz's Autogenic Training helps me. Why this particular video? I can't explain this phenomenon :)
A feeling of incomplete inhalation or a feeling of lack of air is often within the framework of a neurotic disorder (with the exclusion of lung pathology), you focus on inhaling, while this process always occurs reflexively, without our participation. Try breathing exercises or breathing in a paper bag.