Coughing so severe causing difficulty breathing, gagging, throwing up, not able to sleep, so severe has strained back and neck. Should there be concer?

See dr. This is likely post viral cough but you could have whooping cough , not uncommon in adults inspiteof vaccine , check with your local dr.
See your doc. Could be allergy, sinus infection, asthma, pneumonia, blood clots, tumor. Depends on age, risk factors, etc. At the least inhaling steam, fluids, honey may help. Don't know your history re: safety taking decongestants, cough suppressants, etc. See your doc, get relief.