looks the your son has an upper respiratory tract
infection with a gi infection. children do not spit out the sputum. they rather swallow the sputum. so they some times have vomiting
due to thick sputum. i would advise you to take him to a pediatrician
to rule our lower respiratory tract infection.
at home i would advise you to maintain giving him adequate food and water. if you feel he looks dehydrated give him oral rehydration solution every half an hour.
usually immunisation is safe. and the chances of a respiratory infection dude to immunisation is rare. some times babies have fever
due to dpt vaccine
if you feel the symptoms are not subsiding then consult your pediatrician.
wish your son a speedy recovery. take care