I realize this answer may be a little bit late ... but may help someone later.
Ciprodex (Ciprofloxacin-dexamethasone) otic has been assigned to pregnancy category C by the FDA. Animal studies with large oral and intravenous ciprofloxacin have revealed no evidence of embryotoxicity, fetotoxicity, or teratogenicity; however, some maternal toxicity (gastrointestinal disturbances, weight loss, and abortion) was observed. Corticosteroids have demonstrated teratogenicity in animal studies. There are no controlled data in human pregnancy. The manufacturer recommends caution if ciprofloxacin-dexamethasone otic is used during pregnancy.
It is fine to use Ciprodex. The ear infection won't resolve itself, you will need antibiotics of some form, either oral or otic drops. This will help treat the infection and the risks of it causing any harm during pregnancy if very, very, very low.
All the best for your pregnancy.