After researching for even rare side effects, I can say with a high degree of certainty that it is not at all likely that the azithromycin is causing your problem. It is most likely related to your currant infection (http://www.wrongdiagnosis.com/symptoms/night_sweats/causes-common-cold.htm). It was actually even listed in the package insert that when used in combination with Rifabutin (another antibiotic), or when used alone for a serious lung infection called Mycobacterium Avium Complex one of the symptoms of the disease shown to decrease was night sweats.
Hope this helps at least with explanation.
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