How can I help my little guy with this cough and runny nose? Doc can't see him until Monday. He…

How can I help my little guy with this cough and runny nose? Doc can't see him until Monday. He won't take Motrin or Tylenol. He'll make himself throw up of we give it to him. He's sleeping a lot. No fever, he is a little warm but not fever temp. (Tested rectally) He's fine as long as he's calm but he keeps working himself into caughing fits.