If you are being suffocated in a dream, then you may be dealing with a waking situation or person that is causing you to feel crowded, to the point you feel you barely have room or time to breathe. This dream may be a wake up call that you need to either take some responsibilities off your plate or seriously consider distancing yourself from the person that is pressuring or crowding you in real life.
If you are suffocating someone in the dream, then ask yourself what situation in your life or what behavior are you trying to extinguish right now?
If you often wake up from dream or from sleep and you have the sense you are suffocating you could be suffering from Sleep Apnea (consult your doctor) or you are having Sleep Paralysis, which is harmless. With Sleep Paralysis you are in your bed in a half awake half asleep state. You often can’t move and feel pressure on your chest and a sense of suffocation. There is often a sense of a dark presence in the room. it is frightening but only lasts a moment or two and then you suddenly fully awake and are just fine. Fitful sleep will cause this.