Fluid comming out from ear after an episode of cold in small children is mostly almost 99% due to ASOM( ie Acute Suppurative Otitis Media). Due to the cold and nasal Blockage the tube connecting middle ear with back of nose called the Eustachian tube gets blocked and lead to pent up secretions in middle ear which catches infection and after a certain period it perforates the TM and comes like what is happening in your child. But nothing to be worried about a perforated TM heals by itself in children if proper treatment is taken.

Need to know details of history of ear discharge And picture of it

Get the baby examined by an ENT. She may require oral antibiotics etc. Further more kindly follow proper feeding advice specially position of baby while feeding to avoid such issues in future. Also never put oil or any other remedies in babies ear to avoid such problems. Keep her ear dry.

You need to see a ent specialist Discharge from the ear suggests infection Which requires proper treatment and examination of the ear to look for a perforation or a granulation in the ear . Please consult an ent specialist