Getting over cold with thick post nasal drip at night. The past few nights I remember waking up multiple time s to breath. Can drip cause temp apnea?

Sinus infection. About 10% of the time , people with colds end up with a bacterial sinusitis which can cause the symptoms you described. See your family doctor.
Gagging. The drip causes obstruction the breathing through the nose and people breath through the mouth. The back of the throat dries up and people can wake up like gagging and the quality is similar to how people with sleep apnea wake up, but no, it is not real sleep apnea. Drink fluids to loosen the secretion and you may need other meds. See you doctor for treatment.