Can a chiropractic neck adjustment cause throat tightness sensations?

Yes. Chiropractic massage/adjustment is strenuous and should never be allowed on the neck. The back is strong enough usually to withstand it. There have been a number of cases of paralysis, fracture and stroke at the hands of chiros overdoing it on the neck. If your neck troubles you, see an orthopedic specialist for a proper diagnosis and treatment.