Does anyone have experience giving LO antibiotics? How did you feel? Did they work?

My baby girl is just 3 months and was prescribed antibiotics today (for a sinus infection?)...my doctor said "I hate to do this for a baby so young but we've tried everything else". I just feel so unsettled about it!

She has been 'sick' for over a month now (congestion, cough, etc.), it started just 3 days after beginning daycare. We've tried saline and suction, a humidifier, and taking her out of daycare for a week. Nothing. Luckily, tomorrow is her last day of daycare for good but ugh, I hate giving her medicine when she is SO young!