It is colloquial usage. Incorrect but commonly used because the meaning is clear.
Obviously it should be: "You should go to see a doctor", although you'll frequently hear: "You should go and see a doctor". In colloquial English, the conjunction "and" often replaces the "to" with an infinitive verb.
Indeed, "and" is so commonly used in such a context that it has become accepted in books and newspapers.
Student or Learner