I had a fever, blocked nose and sore throat a week ago, I'm fine now except I have to blow my nose all the time and yellow thick phlegm in my cough.

URI. You have the after effects of a viral illness. If the symptoms persist beyond ten days, see your doctor. Antibiotics may be in necessary.
Normal. The last two symptoms to clear after a viral illness are drainage and cough. It may take 2-3 weeks for these to completely clear. If these symptoms persist for a total of 4 weeks then may be low grade sinusitis and need antibiotics to clear.

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