You should make an appointment to see your doctor to check your lungs.
If there is an infection in the lungs the doctor will prescribe an antibiotic for you.
The coughing may be related to the vomiting and if this is the case, the doctor may prescribe medication if you have acid reflux problems.
Make sure that you drink plenty of warm fluids and keep wrapped up warm by wearing a scarf around your mouth and nose so as not to breathe in the cold air when you go outside.
Go to your doctor. You may have a lil fluid in your lungs. Could be bronchidus (caint spell) or a very small possibility you may have accidently inhalled some liguid from the vomit episode. Best bet, go to your doctor. Hope you get well soon.