If your 11-month-old baby has had a fever for three days, is coughing to the point of vomiting, and is very irritable, it is best to consult a doctor. It is recommended to seek medical advice if the fever persists for more than two days or if the child is extremely lethargic, sleepy, or not eating at all. It's important to monitor your child's symptoms closely and seek professional medical advice if needed for proper care and treatment.