Hello, and sorry to hear about your cold and congestion, they just never seem to want to go away. As for your case, I would say that you're safe without an antibiotic. The vast, vast majority of colds are viral, for which antibiotics don't work in the first place, and our bodies are pretty efficient at taking care of these in a couple of weeks. It sounds like you have some left over congestion and drainage, but at this point I wouldn't be concerned about an infection. If I were you, I would try just a nasal saline spray that you can buy at any pharmacy cheap, this will loosen up the sinus secretions, to help insure that the mucus won't have an opportunity to stick around and become infected. Keep an eye out for any changes in color of the mucus, sinus pressure or headaches, and you should be on your way to feeling better soon. Please let me know if you have further questions, best of luck...
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