Dreaming of not breathing means you are suffering or about to suffer great pains at any given moment. Calamity could strike without you knowing. Note your dream with a bit of caution because in the waking hours we all need to breath to live.
Holding your breath in a dream means you have come to a standstill with an adversary. The problem between you both cannot be resolved because neither one of you are willing to give way to the other. Consider letting out some air and continue by opening communication channels. Being more right than the other person is a path to losing for both parties.