If rattling, wheezing noises temporarily clear with coughing, are they coming from the lungs or the throat?

They more likely are coming from the trachea ( windpipe) or from the bronchial tubes. Mucus or mild spasm may be the cause. Have you had a recent head cold? If so, A viral infection is likely. Allergic causes are another possibility. If symptoms worsen instead of gradually improving see your MD for early treatment as asthmatic bronchitis or bronchial asthma are stubborn conditions to eradicate