I have these episodes when i cough and vomit afterwards. should i see a pulmonologist?

Yes: Coughing followed by vomiting could be an infection (we see that with whooping cough). It could also be a sign of gastroesophageal reflux disease. I would recommend evaluation by a primary care physician and let them decide which specialist you should see.

Yes: Coughing can cause vomiting due to gagging from incessant coughing, or else from gastro-esophageal reflux. So need to find the cause of your cough and control your coughing, perhaps with the help of a pulmonologist after seeing your primary care doctor.