3yrs old with cold. Most of the colds in 3 years old are caused by viral infections and are self limiting.If the child has no fever and has just runny nose and cough.You can use saline nose drops followed by having him blow his nose gently or suction it.If in doubt have the child examined by your pediatrician, if the child is sicker, have fever, not eating or drinking and has ear ache or wheezing ets, or cough does not.
Old remedies. Be sure to keep the child well hydrated and comfortable. If the cough is annoying use wild honey based cough medicines (older than 6 months) to soothe the throat and stop the cough. This is safe and may help. If pain is present, use of Acetaminophen or Ibuprofen may help swallowing of fever reduction. Chicken soups is good too.
Cold. Depends on what your child has in the first place but generally speaking, uri's or the common colds are self limited illnesses and we normally don't recommend medicines for it unless your child has asthma and she/he needs the asthma meds.