Baby throwing up

AB

Did your baby ever throw up from being sick/coughing ? My almost one year old baby has a runny nose and coughing, but no fever. Last couple of days he would cough right after drinking his milk and causing him to throw up all his milk. He seems to be in good spirit still but of course I’m very worry as a first time mom. Should I take him in or is this sounds like a flu/stomach flu? He gets sick a lot from the daycare 🤦🏻‍♀️also, last couple of weeks he hasn’t really had the appetite for solids. All he wants is milk.