Ofloxacin (the active ingredient in your prescribed medication) does pass into breast milk in small amounts. While generally considered acceptable to use under medical supervision, it may occasionally cause mild, temporary side effects in your 9-month-old, such as loose stools, diaper rash, or thrush. Serious complications are extremely rare. To minimize your baby's exposure, try taking your dose immediately after a breastfeeding session. Please monitor your baby for any digestive changes. If you remain concerned, you can consult your doctor to see if a more common, breastfeeding-friendly antibiotic alternative is suitable for your sore throat and fever.