Apparently there are no reported FDEs due to
azithromycin. However, other drugs in the same
class, such as erythromycin and clarithromycin, can cause FDE, so for sure azithro could do it. However, it's apparently rare. If your doctor and/or a dermatologist agrees FDE is a good bet, perhaps s/he will want to consider writing up a case report for submission to a medical journal.