I should add that, though it started out the way I said, today its meaning has 'softened', so in your sentence, it is just an informal way of saying "I think you should talk to/see/consult a doctor (about that cough)"
I'd say that this has nothing to do with paying money to the doctor for a visit; rather, it is just a typical way in AmE of saying "We should go and pay the doctor a visit", where the coordinator "and" has been omitted in typical AmE style!
I'd say that this has nothing to do with paying money to the doctor for a visit; rather, it is just a typical way in AmE of saying "We should go and pay the doctor a visit", where the coordinator "and" has been omitted in typical AmE style!